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Mathematics concept
when it refers instead to a structure on vector spaces, it may be called a linear complex structure. A complex structure on a real vector space V {\displaystyle
Linear_complex_structure
Smooth manifold
mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an
Almost_complex_manifold
Topics referred to by the same term
A complex structure may refer to: Almost complex manifold Complex manifold Linear complex structure Generalized complex structure Complex structure deformation
Complex_structure
Mathematics concept
vector addition and real scalar multiplication) with the conjugate linear complex structure J {\displaystyle J} (different multiplication by i {\displaystyle
Complex conjugate of a vector space
Complex_conjugate_of_a_vector_space
Group of 𝑛 × 𝑛 invertible matrices
More generally, the general linear group of degree n {\displaystyle n} over any field F {\displaystyle F} (such as the complex numbers), or a ring R {\displaystyle
General_linear_group
Study of abstract algebraic structures
of the simplest non-trivial examples is a linear complex structure, which is a representation of the complex numbers C, thought of as an associative algebra
Algebra_representation
Data organization and storage formats
alternatively, user-defined) rule for comparing elements. A data structure is said to be linear if its elements form a sequence. Array Associative array Bit
List_of_data_structures
Structure group sub-bundle on a tangent frame bundle
real space of a complex vector space: it admits a linear complex structure. A real vector bundle admits an almost complex structure if and only if it
G-structure_on_a_manifold
Manifold
differential geometry and complex geometry, a complex manifold or a complex analytic manifold is a manifold with a complex structure, that is an atlas of charts
Complex_manifold
Topic in mathematics
the identical space – a real vector space with linear complex structure is identical data to a complex vector space – though it constructs the space differently
Complexification
Several equations of degree 1 to be solved simultaneously
approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.
System_of_linear_equations
Number with a real and an imaginary part
alternative complex structure on R 2 . {\displaystyle \mathbb {R} ^{2}.} This is generalized by the notion of a linear complex structure. Hypercomplex
Complex_number
Topological manifold with a piecewise linear structure on it
a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined
Piecewise_linear_manifold
Literary element
Story structure or narrative structure is the recognizable or comprehensible way in which a narrative's different elements are unified, including in a
Story_structure
Branch of mathematics
vector-space structure. Given two vector spaces V and W over a field F, a linear map (also called, in some contexts, linear transformation or linear mapping)
Linear_algebra
Undeciphered writing system of ancient Crete
contains Linear A Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear A. Linear A is
Linear_A
Algebraic structure in linear algebra
In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled")
Vector_space
Mathematical concept
representation Orthogonal matrix Unitary matrix Hamiltonian mechanics Linear complex structure Williamson theorem Hamiltonian matrix Folland, G. B. (1989). Harmonic
Symplectic_matrix
Integral transform and linear operator
{\displaystyle L^{p}(\mathbb {R} )} , the Hilbert transform defines a linear complex structure on this Banach space. In particular, when p = 2, the Hilbert transform
Hilbert_transform
Number, approximately 3.14
the unique (positive) normalizing factor such that H defines a linear complex structure on the Hilbert space of square-integrable real-valued functions
Pi
Property of a differential manifold that includes complex structures
generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized
Generalized_complex_structure
orthogonal linear complex structure. In general the Cauchy transform is a non-self-adjoint idempotent and the Hilbert transform a non-orthogonal complex structure
Singular integral operators on closed curves
Singular_integral_operators_on_closed_curves
Speech coding algorithm
Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in
Code-excited linear prediction
Code-excited_linear_prediction
Linear map from a vector space to its field of scalars
scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the set of all linear functionals from V to k is itself a
Linear_form
Branch of geometry
symplectic space. This rotation is simply multiply-by-i of the standard linear complex structure on the symplectic space. In the plane, it exchanges a curve and
Contact_geometry
Chemical compound of a transition metal and nitric oxide
linear NO ligands are equivalent to three CO groups. This trend is illustrated by the isoelectronic pair Fe(CO)2(NO)2 and [Ni(CO)4]. These complexes are
Metal_nitrosyl_complex
Operation in algebra
can be interpreted either as a complex vector space (S-module) or as a real vector space with a linear complex structure (algebra representation of S as
Change_of_rings
Set of vectors used to define coordinates
structures and frames of reference. A basis B of a vector space V over a field F (such as the real numbers R or the complex numbers C) is a linearly independent
Basis_(linear_algebra)
Mathematical structure in abstract algebra
conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert
*-algebra
Statistical method
maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable
Partial least squares regression
Partial_least_squares_regression
Algebraic structure
In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge
Hodge_structure
Statistical modeling method
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory
Linear_regression
Mathematical set with some added structure
retains the same mathematical structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces
Space_(mathematics)
Construction in group theory
the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector
Projective_linear_group
Type of vector space in math
x,x\rangle } is a real number. The inner product is linear in its first argument. For all complex numbers a {\displaystyle a} and b , {\displaystyle b
Hilbert_space
1966 mathematics textbook by Serge Lang
Linear Algebra is a 1966 mathematics textbook by Serge Lang. The third edition of 1987 covers fundamental concepts of vector spaces, matrices, linear
Linear_Algebra_(book)
System where changes of output are not proportional to changes of input
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change
Nonlinear_system
Mathematics concept
In mathematics, a real structure on a complex vector space is a way to decompose the complex vector space in the direct sum of two real vector spaces
Real_structure
Mathematical function, in linear algebra
In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which
Linear_map
Differentiable manifold
differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an
CR_manifold
System composed of many interacting components
deterministic; (iii) mathematical models of the system are usually complex and involve non-linear, ill-posed, or chaotic behavior; (iv) the systems are predisposed
Complex_system
Method to solve optimization problems
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical
Linear_programming
Geometric structure on a smooth manifold
codimension-one linear subspace Q p {\displaystyle Q_{p}} of the tangent space T p M {\displaystyle T_{p}M} ), a linear complex structure on it (that is, a linear function
Almost_contact_manifold
Ring that is also a vector space or a module
the result should be a linear representation of the same algebra on the product vector space. Imposing such additional structure typically leads to the
Associative_algebra
Concept in geometry
to the situation for complex manifolds, which always have a globally defined almost complex structure. A quaternionic structure on a smooth manifold M
Quaternionic_manifold
Representation of mathematical space
triangulable space. Triangulations can also be used to define a piecewise linear structure for a space, if one exists. Triangulation has various applications
Triangulation_(topology)
Vector space equipped with a bilinear product
set in the complex plane. These are also commutative. Incidence algebras are built on certain partially ordered sets. algebras of linear operators, for
Algebra_over_a_field
Notation for quantum states
notation or Dirac notation is a mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual spaces both in
Bra–ket_notation
Sum of elements on the main diagonal
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle
Trace_(linear_algebra)
Lie group whose manifold is complex and whose group operation is holomorphic
the structure of a complex Lie group. A complex semisimple Lie group is a linear algebraic group. The Lie algebra of a complex Lie group is a complex Lie
Complex_Lie_group
Subgroup of the group of invertible n×n matrices
viewed as linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded as a linear algebraic
Linear_algebraic_group
Mathematical group
mathematics, the symplectic group is the group of linear transformations that preserve the geometric structure of phase space, the space of position and momentum
Symplectic_group
Mathematical form
composition of two linear mappings between finite dimensional vector spaces. Let the linear mapping f map V to W, and let the linear mapping g map W to
Product_(mathematics)
Function acting on function spaces
most important cases are sequences of real or complex numbers, and these spaces, together with linear subspaces, are known as sequence spaces. Operators
Operator_(mathematics)
Universal construction of a complex Lie group from a real Lie group
group it can be realized concretely as a closed subgroup of the complex general linear group. It consists of operators with polar decomposition g = u •
Complexification_(Lie_group)
Group that is also a differentiable manifold with group operations that are smooth
in quantum mechanics In loc. cit., a linear Lie group is defined as an immersed subgroup of the general linear group GL ( n , C ) {\displaystyle \operatorname
Lie_group
In projective geometry, a bijection between projective spaces that preserves collinearity
projective semi-linear structure". Correspondingly, the quotient group PΓL / PGL ≅ Gal(K/k) corresponds to "choices of linear structure", with the identity
Collineation
Number of atoms in a ligand that bond to the central atom of a coordination complex
in a given ligand that bind to the central metal atom in a coordination complex. In many cases, only one atom in the ligand binds to the metal, so the
Denticity
Array of numbers
widely applied in simulating complex physical systems. It attempts to approximate the solution to some equation by piecewise linear functions, where the pieces
Matrix_(mathematics)
Archaeological site and Minoan palace complex in Heraklion, Crete
Ancient Greek: Κνωσσός, romanized: Knōssós; Greek: Κνωσός, romanized: Knōsós; Linear B: 𐀒𐀜𐀰 Ko-no-so) is an archaeological site and ancient urban centre in
Knossos
Space of complex matrices with positive definite imaginary part
{\displaystyle \omega } . A compatible complex structure on V {\displaystyle V} is a linear complex structure on V {\displaystyle V} , such that ω ( J
Siegel_upper_half-space
Anions composed of many iodine atoms
diverse structures. Most can be considered as associations of I2, I−, and I− 3 units. Discrete polyiodides are usually linear. The more complex two- or
Polyiodide
Algebraic curve in mathematics
structure of the torus. However, all real polynomials factorize completely into linear factors over the complex numbers, since the field of complex numbers
Elliptic_curve
Fundamental principle of physics
superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the
Superposition_principle
Manifold with Riemannian, complex and symplectic structure
manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by
Kähler_manifold
Flaw in mathematical modelling
Replacing this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent variables
Overfitting
Group of unitary matrices
of matrix multiplication. The unitary group is a subgroup of the general linear group GL ( n , C ) {\displaystyle \operatorname {GL} (n,\mathbb {C} )}
Unitary_group
Branch of mathematics
variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It
Algebra
Narrative technique
utilizes a non-linear structure, focusing on events throughout the life of the titular character rather than describing them in a linear narrative. From
Nonlinear_narrative
Archaeological horizon of Neolithic Europe
large Rondel complexes were discovered east of the Vistula River near Toruń in Poland. A number of cultures ultimately replaced the Linear Pottery culture
Linear_Pottery_culture
Branch of mathematics that studies abstract algebraic structures
algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In
Representation_theory
System of resource-aware logic
Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities
Linear_logic
Intermolecular attraction between a hydrogen donor-and-acceptor pair
bonds also affect the aramid fibre, where hydrogen bonds stabilize the linear chains laterally. The chain axes are aligned along the fibre axis, making
Hydrogen_bond
Algebraic variety with a group structure
are linear groups or abelian varieties; for instance, some group schemes occurring naturally in arithmetic geometry are neither. Chevalley's structure theorem
Algebraic_group
Mathematical concept
imaginary part of the standard complex (Hermitian) inner product on Cn (with the convention of the first argument being anti-linear). Let ω be an alternating
Symplectic_vector_space
algebraic structure of linear algebra Field – algebraic structure with addition, multiplication and division Groups – algebraic structure with a single
Outline_of_algebra
Most widely known generalized inverse of a matrix
In mathematics, and in particular linear algebra, the Moore–Penrose inverse A + {\displaystyle A^{+}} of a matrix A {\displaystyle A} , often called
Moore–Penrose_inverse
Line of thunderstorms along or ahead of a cold front
(which often are accompanied by abrupt and gusty wind shifts). Linear thunderstorm structures often contain heavy precipitation, hail, frequent lightning
Squall_line
Unsolved problem in geometry
non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties
Hodge_conjecture
Atomically-precise manufacturing system
atomically precise structures (that is, virtually defect-free) do not exist. Complex 3D nanoscale structures exist in the form of folded linear molecules such
Productive_nanosystems
Group of unitary complex matrices with determinant of 1
\operatorname {M} (2,\mathbb {C} )} denotes the set of 2 by 2 complex matrices, is an injective real linear map (by considering C 2 {\displaystyle \mathbb {C} ^{2}}
Special_unitary_group
Mathematical model of the time dependence of a point in space
simple trigonometric functions (i.e. complex exponentials), and the behavior of all orbits can be classified. In a linear system the phase space is the N-dimensional
Dynamical_system
Fundamental operation on complex numbers
} is a R {\textstyle \mathbb {R} } -linear transformation of V , {\textstyle V,} if one notes that every complex space V {\displaystyle V} has a real
Complex_conjugate
Type of particle accelerator
A linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high
Linear_particle_accelerator
Affine space over the complex numbers
example is the Argand plane of complex numbers C {\displaystyle \mathbb {C} } itself. This has a canonical linear structure, and so "forgetting" the origin
Complex_affine_space
Type of transport in differential geometry
da^{i}+\zeta \wedge a^{i}+a^{k}\wedge a_{k}^{i}=0} A projective structure is a linear geometry on a manifold in which two nearby points are connected
Projective_connection
Euclidean space without distance and angles
same linear combination, despite using different origins. While only Alice knows the "linear structure", both Alice and Bob know the "affine structure"—i
Affine_space
2D surface which extends indefinitely
collinearity. Conversely, in adding more structure, one may view the plane as a 1-dimensional complex manifold, called the complex line. Many fundamental tasks in
Plane_(mathematics)
Biological process
this process creates a "theta structure" (resembling the Greek letter theta: θ). In contrast, eukaryotes have longer linear chromosomes and initiate replication
DNA_replication
{\displaystyle J_{x}^{2}=-1} as a linear map. If E {\displaystyle E} is a complex vector bundle, then the complex structure J {\displaystyle J} can be defined
Complex_vector_bundle
Elements of a field, e.g. real numbers, in the context of linear algebra
modules is a special case of scaling, a kind of linear transformation. Algebraic structure Scalar (physics) Linear algebra Matrix (mathematics) Row and column
Scalar_(mathematics)
Concepts from linear algebra
negative or complex number). Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation
Eigenvalues_and_eigenvectors
Study of the response of buildings and structures to earthquakes
spectrum approach is no longer appropriate, and more complex analysis is often required, such as non-linear static analysis or dynamic analysis. Static procedures
Seismic_analysis
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
simple or 'close' to being simple: for example, the so-called "special linear group" SL(n, R {\displaystyle \mathbb {R} } ) of n by n matrices with determinant
Simple_Lie_group
Method for estimating new data outside known data points
periodic, etc. Linear extrapolation means creating a tangent line at the end of the known data and extending it beyond that limit. Linear extrapolation
Extrapolation
Routines for performing common linear algebra operations
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations
Basic Linear Algebra Subprograms
Basic_Linear_Algebra_Subprograms
Algebraic structure with addition, multiplication, and division
operations on rational numbers do. A field is thus a fundamental algebraic structure that is widely used in algebra, number theory, and many other areas of
Field_(mathematics)
Reverse-engineering neural networks
explanations. This hypothesis suggests that high-level concepts are represented as linear directions in the activation space of neural networks. Empirical evidence
Mechanistic_interpretability
Branch of mathematics
algebraic structure, such as associativity (to form semigroups); identity, and inverses (to form groups); and other more complex structures. With additional
Abstract_algebra
vector spaces over the normed fields of real or complex numbers in functional analysis." The term "linear topology" goes back to Lefschetz's work. For each
Linear_topology
LINEAR COMPLEX-STRUCTURE
LINEAR COMPLEX-STRUCTURE
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).
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Boy/Male
Hindu
Lingam
Girl/Female
Bengali, Indian
Good Complex
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
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."
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’.
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
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.
Surname or Lastname
English
English : occupational name for a whitewasher, Middle English limer, lymer, an agent derivative of Old English līm ‘lime’.
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.
Girl/Female
Hindu, Indian
Complex
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Surname or Lastname
English
English : metronymic from Line.
LINEAR COMPLEX-STRUCTURE
LINEAR COMPLEX-STRUCTURE
Girl/Female
Greek
White as milk. In mythology Pygmalion fell in love with the statue Galatia and Aphrodite brought...
Boy/Male
Hindi
Nation.
Boy/Male
Indian, Punjabi, Sikh
Light of the Lord
Boy/Male
Hindu, Indian
Knowledgeable
Boy/Male
Tamil
Couple
Surname or Lastname
English
English : unexplained. It has been suggested that it may be a French Huguenot name, possibly an altered form of Ruvigny.
Girl/Female
Hindu, Indian, Marathi
Plenty; Strong
Boy/Male
Greek
Name of a philosopher.
Boy/Male
Indian, Tamil
Brilliant Like Sun
Boy/Male
Indian, Tamil
God Krishna
LINEAR COMPLEX-STRUCTURE
LINEAR COMPLEX-STRUCTURE
LINEAR COMPLEX-STRUCTURE
LINEAR COMPLEX-STRUCTURE
LINEAR COMPLEX-STRUCTURE
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
a.
Linear.
imp. & p. p.
of Couple
imp. & p. p.
of Compile
adv.
In a linear manner; with lines.
a.
Of a linear shape.
a.
Composed of lines; delineated; as, lineal designs.
a.
Intricate; entangled; complicated; complex.
a.
Not complex; uncompounded; simple.
n.
A complex; an aggregate of parts; a complication.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
imp. & p. p.
of Comply
n.
Two taken together; a pair or couple; especially two lines of verse that rhyme with each other.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Complex, complicated.
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 lines, as, a liner of shoes.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
a.
Repeatedly compound; made up of complex constituents.
adv.
In a complex manner; not simply.