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In mathematics, vector subspace
specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually
Linear_subspace
Algebraic structure in linear algebra
are linearly independent if a linear combination results in the zero vector if and only if all its coefficients are zero. Linear subspace A linear subspace
Vector_space
Linear subspace generated from a vector acted on by a power series of a matrix
In linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images
Krylov_subspace
Vectors mapped to 0 by a linear map
vector of the co-domain; the kernel is always a linear subspace of the domain. That is, given a linear map L : V → W between two vector spaces V and W
Kernel_(linear_algebra)
Euclidean space without distance and angles
a linear subspace (vector subspace) of a vector space produces an affine subspace of the vector space. One commonly says that this affine subspace has
Affine_space
Subspace preserved by a linear mapping
In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by
Invariant_subspace
Mathematical set with some added structure
affine subspace of A is the intersection of A with a (k+1)-dimensional linear subspace of L that intersects A. Every point of the affine subspace A is the
Space_(mathematics)
In linear algebra, generated subspace
V} is the smallest linear subspace of V {\displaystyle V} that contains S . {\displaystyle S.} It is the set of all finite linear combinations of the
Linear_span
Theorem on extension of bounded linear functionals
central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space. The theorem
Hahn–Banach_theorem
Topics referred to by the same term
space A subset of a topological space endowed with the subspace topology Linear subspace, in linear algebra, a subset of a vector space that is closed under
Subspace
Branch of mathematics
mathematical structures. These subsets are called linear subspaces. More precisely, a linear subspace of a vector space V over a field F is a subset W
Linear_algebra
Mathematical function, in linear algebra
{\displaystyle V} ). A linear mapping always maps the origin of V {\displaystyle V} to the origin of W {\displaystyle W} , and linear subspaces of V {\displaystyle
Linear_map
Normed vector space that is complete
the null space. The closed linear subspace M {\displaystyle M} of X {\displaystyle X} is said to be a complemented subspace of X {\displaystyle X} if M
Banach_space
Vector space with generalized dot product
{\displaystyle {\overline {H}}.} This means that H {\displaystyle H} is a linear subspace of H ¯ , {\displaystyle {\overline {H}},} the inner product of H {\displaystyle
Inner_product_space
Idempotent linear transformation from a vector space to itself
subspace always has a closed complementary subspace. This is an immediate consequence of Hahn–Banach theorem. Let U {\displaystyle U} be the linear span
Projection_(linear_algebra)
Completion of the usual space with "points at infinity"
textbooks. Using linear algebra, a projective space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one)
Projective_space
Fundamental space of geometry
subspaces: its Euclidean subspaces and its linear subspaces. Linear subspaces are Euclidean subspaces and a Euclidean subspace is a linear subspace if
Euclidean_space
Vector space consisting of affine subsets
In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace U {\displaystyle U} is a vector space obtained by "collapsing" U {\displaystyle
Quotient space (linear algebra)
Quotient_space_(linear_algebra)
Type of vector space in math
Hilbert space. At a deeper level, perpendicular projection onto a linear subspace plays a significant role in optimization problems and other aspects
Hilbert_space
the elements of W are all zero. 2. Orthogonal subspace in the dual space: If W is a linear subspace (or a submodule) of a vector space (or of a module)
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Concept in integration theory
{d} x^{n}} Consider the linear subspace of the n-dimensional Euclidean space Rn that is spanned by a collection of linearly independent vectors X 1
Volume_element
Dimension of the column space of a matrix
{\displaystyle M} is a linear subspace then dim ( A M ) ≤ dim ( M ) {\displaystyle \dim(AM)\leq \dim(M)} ; apply this inequality to the subspace defined by the
Rank_(linear_algebra)
Linear map from a vector space to its field of scalars
{R} } is a linear functional on a linear subspace M ⊆ X {\displaystyle M\subseteq X} which is dominated by p on M, then there exists a linear extension
Linear_form
In mathematics, vector space of linear forms
for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the continuous dual space
Dual_space
Filtering technique
In signal processing, signal subspace methods are empirical linear methods for dimensionality reduction and noise reduction. These approaches have attracted
Signal_subspace
Several equations of degree 1 to be solved simultaneously
These are exactly the properties required for the solution set to be a linear subspace of Rn. In particular, the solution set to a homogeneous system is the
System_of_linear_equations
Mathematical concept
by symplectic matrices. Let W be a linear subspace of V. Define the symplectic complement of W to be the subspace W ⊥ = { v ∈ V ∣ ω ( v , w ) = 0 for
Symplectic_vector_space
Partially unsolved problem in mathematics
H} has a non-trivial closed T {\displaystyle T} -invariant subspace: a closed linear subspace W {\displaystyle W} of H {\displaystyle H} , which is different
Invariant_subspace_problem
Sum of terms, each multiplied with a scalar
assertion "the set of all linear combinations of v1,...,vn always forms a subspace". However, one could also say "two different linear combinations can have
Linear_combination
Concepts from linear algebra
vectors). Because every nullspace is a linear subspace of the domain, E {\displaystyle E} is a linear subspace of C n {\displaystyle \mathbb {C} ^{n}}
Eigenvalues_and_eigenvectors
Vector space equipped with a bilinear product
algebra over a field K is a linear subspace that has the property that the product of any two of its elements is again in the subspace. In other words, a subalgebra
Algebra_over_a_field
Conjugate transpose of an operator in infinite dimensions
{\displaystyle G^{\text{cl}}(A)} is a (closed) linear subspace, the word "function" may be replaced with "linear operator". For the same reason, A {\displaystyle
Hermitian_adjoint
Subspace defined by a polynomial of degree 2 over a field
quadrics is the study of the linear spaces that they contain. (In the context of projective geometry, a linear subspace of P N {\displaystyle {\mathbf
Quadric_(algebraic_geometry)
Approach to dimensionality reduction
generalizations of linear subspace learning methods such as principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis
Multilinear_subspace_learning
Concept in linear algebra
In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W {\displaystyle W} of a vector space V
Orthogonal_complement
In mathematics, in linear algebra and functional analysis, a cyclic subspace is a certain special subspace of a vector space associated with a vector
Cyclic_subspace
Type of geometric transformation
transformation which replaces a subspace of a given space with the space of all directions pointing out of that subspace. For example, the blowup of a point
Blowing_up
Algebraic structure used in analysis
also for groups) has analogs for Lie algebras. A Lie subalgebra is a linear subspace h ⊆ g {\displaystyle {\mathfrak {h}}\subseteq {\mathfrak {g}}} which
Lie_algebra
Number of values in the final calculation of a statistic that are free to vary
context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the number
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Examples of vector spaces Linear map Shear mapping or Galilean transformation Squeeze mapping or Lorentz transformation Linear subspace Row and column spaces
Outline_of_linear_algebra
Machine learning technique
the ReFT family is low-rank linear subspace ReFT (LoReFT), which intervenes on hidden representations in the linear subspace spanned by a low-rank projection
Fine-tuning_(deep_learning)
Projection of data onto lower-dimensional manifolds
diffeomorphic mapping which transports the data onto a lower-dimensional linear subspace. The methods solves for a smooth time indexed vector field such that
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Vector spaces associated to a matrix
space of an m × n matrix with components from F {\displaystyle F} is a linear subspace of the m-space F m {\displaystyle F^{m}} . The dimension of the column
Row_and_column_spaces
Mathematical device used in statistical mechanics
This projection operator acts in the linear space of phase space functions and projects onto the linear subspace of "slow" phase space functions. It was
Zwanzig_projection_operator
Mathematical operation on vector spaces
1 on ( v , w ) {\displaystyle (v,w)} and 0 otherwise. Let R be the linear subspace of L that is spanned by the relations that the tensor product must
Tensor_product
invariant subspace theorem is a mathematical theorem from functional analysis concerning the existence of invariant subspaces of a linear operator on
Lomonosov's invariant subspace theorem
Lomonosov's_invariant_subspace_theorem
Number of vectors in any basis of the vector space
space consisting only of its zero element. If W {\displaystyle W} is a linear subspace of V {\displaystyle V} , then dim ( W ) ≤ dim ( V ) . {\displaystyle
Dimension_(vector_space)
Vector space with a notion of nearness
every topological vector space can be completed and is thus a dense linear subspace of a complete topological vector space. Every TVS has a completion
Topological_vector_space
mathematics, the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by commutators
Commutator_subspace
Theorem
linear operator defined on a dense linear subspace of X. The Hille–Yosida theorem provides a necessary and sufficient condition for a closed linear operator
Hille–Yosida_theorem
Linear operator defined on a dense linear subspace
should be understood as "linear operator" (as in the case of "bounded operator"); the domain of the operator is a linear subspace, not necessarily the whole
Unbounded_operator
Branch of mathematics that studies abstract algebraic structures
of (say) a group G {\displaystyle G} , and W {\displaystyle W} is a linear subspace of V {\displaystyle V} that is preserved by the action of G {\displaystyle
Representation_theory
Difference between the dimensions of mathematical object and a sub-object
space (in isolation)", only the codimension of a vector subspace. If W is a linear subspace of a finite-dimensional vector space V, then the codimension
Codimension
In numerical linear algebra, a Jacobi rotation is a rotation, Qkℓ, of a 2-dimensional linear subspace of an n-dimensional inner product space, chosen to
Jacobi_rotation
Area of mathematics
that every bounded linear operator on a Hilbert space has a proper invariant subspace. Many special cases of this invariant subspace problem have already
Functional_analysis
Affine subspace of a Euclidean space
surfaces, which are subspaces having different notions of distance: arc length and geodesic length, respectively. Flats occur in linear algebra, as geometric
Flat_(geometry)
Method for estimating the unknown parameters in a linear regression model
estimated within some linear subspace of the full parameter space Rp). See partial least squares regression. Methods for fitting linear models with multicollinearity
Ordinary_least_squares
Equation that does not involve powers or products of variables
term linear for describing this type of equation. More generally, the solutions of a linear equation in n variables form a hyperplane (a subspace of dimension
Linear_equation
Subspace of n-space whose dimension is (n-1)
an affine subspace of codimension 1 in an affine space. In Cartesian coordinates, such a hyperplane can be described with a single linear equation of
Hyperplane
In geometry, set whose intersection with every line is a single line segment
{\displaystyle \operatorname {rec} A\cap \operatorname {rec} B} is a linear subspace. If A or B is locally compact then A − B is closed. The notion of convexity
Convex_set
Branch of algebraic geometry
closed sets in a Grassmannian defined by conditions of incidence of a linear subspace in projective space with a given flag. For further details see Schubert
Schubert_calculus
Order whose elements are all comparable
length of chains of subspaces. For example, the dimension of a vector space is the maximal length of chains of linear subspaces, and the Krull dimension
Total_order
Method used in statistics, pattern recognition, and other fields
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization
Linear_discriminant_analysis
Theorem on eigenvalues and eigenvectors of Hermitian matrices
the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B. The theorem is named after Henri Poincaré
Poincaré_separation_theorem
Class of error-correcting code
corrected. This code contains 24 = 16 codewords. A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space F q n
Linear_code
Numerical approximation algorithm
system of linear equations, the two main classes of iterative methods are the stationary iterative methods, and the more general Krylov subspace methods
Iterative_method
Mathematical set closed under positive linear combinations
its extremal rays. For a vector space V {\displaystyle V} , every linear subspace of V {\displaystyle V} is a convex cone. In particular, the space V
Convex_cone
Mathematical space
that parameterizes the set of all k {\displaystyle k} -dimensional linear subspaces of an n {\displaystyle n} -dimensional vector space V {\displaystyle
Grassmannian
projection error, controlling the error of approximation by a linear subspace based on a linear projection relative to the optimal error together with the
Lebesgue's_lemma
Kind of linear transformation
{\displaystyle A\in B(X,Y)} the kernel of A {\displaystyle A} is a closed linear subspace of X {\displaystyle X} . If B ( X , Y ) {\displaystyle B(X,Y)} is Banach
Bounded_operator
Vector space of infinite sequences
functions and pointwise scalar multiplication. All sequence spaces are linear subspaces of this space. Sequence spaces are typically equipped with a norm,
Sequence_space
Type of linear error-correcting code
terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F24 2 of 24-bit words such that any two distinct
Binary_Golay_code
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
therefore the dimension of the corresponding invariant subspace. If all elementary divisors are linear, A is diagonalizable. The Jordan form of a n × n matrix
Jordan_normal_form
Mathematics of smooth surfaces
to consist of all tangent vectors to S at p, is a two-dimensional linear subspace of ℝ3; it is often denoted by TpS. The normal space to S at p, which
Differential geometry of surfaces
Differential_geometry_of_surfaces
Topics referred to by the same term
field Linear keyspace (AKA flat key space), the property of a cipher with no weak keys Linear dimension, a 1D subspace in physical space Linear eccentricity
Linear_(disambiguation)
Function between topological vector spaces
sets Positive linear functional Topologies on spaces of linear maps Unbounded operator – Linear operator defined on a dense linear subspace Narici & Beckenstein
Continuous_linear_operator
Group of 𝑛 × 𝑛 invertible matrices
In mathematics, the general linear group of degree n {\displaystyle n} is the set of n × n {\displaystyle n\times n} invertible matrices, together with
General_linear_group
Vectors whose linear combinations are nonzero
if these subspaces are linearly independent and M 1 + ⋯ + M d = X . {\displaystyle M_{1}+\cdots +M_{d}=X.} Matroid – Abstraction of linear independence
Linear_independence
Type of complex number
{\displaystyle \beta \neq 0} ) α / β {\displaystyle \alpha /\beta } , is a linear subspace of the finite-degree field extension Q ( α , β ) {\displaystyle \mathbb
Algebraic_number
Partial differential equation describing the evolution of temperature in a region
_{mn}} Finally, the sequence {en}n ∈ N spans a dense linear subspace of L2((0, L)). This shows that in effect we have diagonalized the operator
Heat_equation
Algorithms for solving convex optimization problems
minimize cTx s.t. x in {b+L} ∩ K, where b is a vector in Rn, L is a linear subspace in Rn (so b+L is an affine plane), and K is a closed pointed convex
Interior-point_method
Model of n-dimensional hyperbolic geometry
linear subspace (a plane through the origin) of the n+1-dimensional Minkowski space. If we take u and v to be basis vectors of that linear subspace with
Hyperboloid_model
Linear operator whose graph is closed
{\displaystyle X} . To stay useful, they are instead defined on a proper but dense subspace, which still allows approximating any vector and keeps key tools (closures
Closed_linear_operator
"Small" subset of a topological space
doi:10.4064/sm-3-1-174-179. Willard 2004, Theorem 25.5. "Are proper linear subspaces of Banach spaces always meager?". "Research problems" (PDF). Archived
Meagre_set
Points of small height in projective space lie in a finite number of hyperplanes
obtained by Wolfgang M. Schmidt (1972). The subspace theorem states that if L1,...,Ln are linearly independent linear forms in n variables with algebraic coefficients
Subspace_theorem
Mathematical space with a notion of closeness
functions Linear subspace – In mathematics, vector subspace Pointless topology Quasitopological space – Function in topology Relatively compact subspace – Subset
Topological_space
Algebra associated to any vector space
weighted k-dimensional linear subspaces of V {\displaystyle V} . In particular, the Grassmannian of k-dimensional subspaces of V {\displaystyle V}
Exterior_algebra
Description in Riemannian geometry
σ p ) {\displaystyle K(\sigma _{p})} depends on a two-dimensional linear subspace σ p {\displaystyle \sigma _{p}} of the tangent space at a point p {\displaystyle
Sectional_curvature
Concept in functional analysis
functional analysis, a complemented subspace of a topological vector space X , {\displaystyle X,} is a vector subspace M {\displaystyle M} for which there
Complemented_subspace
Type of continuity of a complex-valued function
continuous arcs with α > 1/2, is a linear subspace. There are closed additive subgroups of H, not linear subspaces, connected by 1/2–Hölder continuous
Hölder_condition
Process of reducing the number of random variables under consideration
through multilinear subspace learning. The main linear technique for dimensionality reduction, principal component analysis, performs a linear mapping of the
Dimensionality_reduction
Set of vectors used to define coordinates
bases of subspaces Proof that any subspace basis has same number of elements "Linear combinations, span, and basis vectors". Essence of linear algebra
Basis_(linear_algebra)
Sum of directed areas in exterior algebra
scalars and bivectors. It has dimension 2n−1, and contains ⋀2Rn as a linear subspace. In two and three dimensions the even subalgebra contains only scalars
Bivector
Vector satisfying some of the criteria of an eigenvector
_{i}I)} generate a Jordan chain of linearly independent generalized eigenvectors which form a basis for an invariant subspace of V {\displaystyle V} . Using
Generalized_eigenvector
Subgroup of the group of invertible n×n matrices
P2 of lines (1-dimensional linear subspaces) in A3; and the dual projective space P2 of planes in A3. A connected linear algebraic group G over an algebraically
Linear_algebraic_group
Generalizations of codimension-1 subvarieties of algebraic varieties
divisors linearly equivalent to D, called the complete linear system of D. A projective linear subspace of this projective space is called a linear system
Divisor_(algebraic_geometry)
Theorem in the representation theory of linear algebraic groups
nonzero finite-dimensional vector space V, then there is a 1-dimensional linear subspace L of V such that ρ ( G ) ( L ) = L . {\displaystyle \rho (G)(L)=L.}
Lie–Kolchin_theorem
Function of two vectors linear in each argument
scalar 0 "outside", in front of B, by linearity. The set L(V, W; X) of all bilinear maps is a linear subspace of the space (viz. vector space, module)
Bilinear_map
Geometric space whose points represent algebro-geometric objects of some fixed kind
{\displaystyle V} is the moduli space of all k {\displaystyle k} -dimensional linear subspaces of V. Whenever there is an embedding of a scheme X {\displaystyle X}
Moduli_space
In linear algebra, relation between 3 dimensions
When T : V → W {\displaystyle T:V\to W} is a linear transformation between two finite-dimensional subspaces, with n = dim ( V ) {\displaystyle n=\dim(V)}
Rank–nullity_theorem
LINEAR SUBSPACE
LINEAR SUBSPACE
Surname or Lastname
English
English : occupational name for a whitewasher, Middle English limer, lymer, an agent derivative of Old English līm ‘lime’.
Surname or Lastname
English
English : variant of Lanier 1.Dutch : variant of Leonard.Jewish (western Ashkenazic) : name taken by someone who was good at chanting the Pentateuch at public worship in the synagogue or who regularly did so, from West Yiddish layner ‘reader’ (a derivative of West Yiddish laynen ‘to read’, which comes ultimately from Latin legere ‘to read’).Jewish (Ashkenazic) : occupational name for a flax grower or merchant, from German Lein ‘flax’ + agent suffix -er.
Surname or Lastname
English (Cornish)
English (Cornish) : habitational name from a place named with Cornish lan ‘church’. In England this surname is now found chiefly in the southern counties of Wiltshire and Hampshire, and Berkshire; it has no doubt moved there from Cornwall.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Surname or Lastname
English
English : metronymic from Line.
Boy/Male
Hindu
Lingam
Girl/Female
Irish
Eimear possessed the “Six Gifts of Womanhood†– “beauty, a gentle voice, sweet words, wisdom, needlework and chastity!†She was bethrothed to the warrior Cuchulainn (read the legend) when they were children and they loved each other very deeply. But Cuchulainn had “a wandering eye†and Eimear endured this, realizing “everything new is fair,†but when he made love to Fand, wife of the sea god Manannan, Eimear confronted the lovers. After seeing the strength of Fand’s love she offered to withdraw. Touched by this display of unselfishness, Fand left Cuchulainn and returned to the sea. When Cuchulainn died Eimear spoke movingly and lovingly at his graveside.
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Surname or Lastname
English
English : habitational name from Lingart, Lancashire, or Lingards Wood in Marsden, West Yorkshire, both named from Old English līn ‘flax’ + garðr ‘enclosure’.
Boy/Male
Hindu
The Sun
Female
English
English name probably derived from Germanic lindi, LINDA means "serpent."Â In some cases, it may have been derived from the Spanish word for "pretty."
Surname or Lastname
English
English : variant of Lingard.French : occupational name for a maker of or dealer in linen goods, from Old French linge ‘linen (goods)’ (see Linge 1).
Surname or Lastname
English (Devon; of Cornish origin)
English (Devon; of Cornish origin) : topographic name for someone who lived by a menhir, i.e. a tall standing stone erected in prehistoric times (Cornish men ‘stone’ + hir ‘long’).
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Boy/Male
Irish
Meaning “â€fair-haired,â€â€ the name has been popular since the sixth century when St. Finbar came to an area of Cork that was being tormented by a serpent. The people begged him to do something to help them. One night he went to where the serpent was sleeping and sprinkled it with holy water. The angry serpent tore and devoured the land until she slithered into the sea at Cork Harbor. The track she left behind filled with water and became the River Lee and that’s why St. Finbar is the patron saint of Cork. It is said that the sun didn’t set for two weeks after Finbar’s death.
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
Boy/Male
Sikh
Love unending
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Surname or Lastname
Swedish
Swedish : ornamental name from lind ‘lime tree’ + either the German suffix -er denoting an inhabitant, or the surname suffix -ér, derived from the Latin adjectival ending -er(i)us.English (mainly southeastern) : variant of Lind 2.German : habitational name from any of numerous places called Linden or Lindern, named with German Linden ‘lime trees’.
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
LINEAR SUBSPACE
LINEAR SUBSPACE
Girl/Female
Hindu, Indian, Tamil
Beautiful Gem
Boy/Male
Arabic, Celebrity, Farsi, German, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Pashtun, Sanskrit, Sindhi, Tamil, Telugu
Pious; Honest; Obedient; Head of a Group; The Marcasite Stone; Heavenly; Better Guided
Boy/Male
Irish
Happy.
Boy/Male
Tamil
Parthu | பாரà¯à®¤à¯à®‚
Boy/Male
Arabic, Muslim
Time
Surname or Lastname
German (Mäule)
German (Mäule) : variant of Maul 1.English : variant of Maul 2.
Boy/Male
Tamil
Relation
Girl/Female
Hindu
Creeper of Love, Vine of Love
Surname or Lastname
German
German : reduced form of Widmer.German : occupational name from Middle High German wimmer ‘wine maker’.German : nickname from Middle High German wim(m)er ‘knotty growth on a tree trunk’.German : variant of Weimer 2.English : from the Old English personal name Winemǣr, a compound of wine ‘friend’ + mǣr ‘famous’.
Boy/Male
Tamil
Sindhunath | ஸிநà¯à®¤à¯à®¨à®¾à®¤
Lord of the ocean
LINEAR SUBSPACE
LINEAR SUBSPACE
LINEAR SUBSPACE
LINEAR SUBSPACE
LINEAR SUBSPACE
a.
Formed by right lines; rectilineal; as, a right-lined angle.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
a.
Composed of lines; delineated; as, lineal designs.
n.
One who lines, as, a liner of shoes.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
n.
One who adjusts things to a line or lines or brings them into line.
prep. & adv.
Near.
n.
Alt. of Lingam
a.
Of a linear shape.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.
a.
Linear.
v. t.
To mark with a line or lines; to cover with lines; as, to line a copy book.
n.
A lunar distance.
adv.
In a linear manner; with lines.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
n.
A dealer in linen; a linen draper.
v. t.
To convert into vinegar; to make like vinegar; to render sour or sharp.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
n.
Made of linen; as, linen cloth; a linen stocking.
n.
A vessel belonging to a regular line of packets; also, a line-of-battle ship; a ship of the line.