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mathematics, in linear algebra and functional analysis, a cyclic subspace is a certain special subspace of a vector space associated with a vector in the vector
Cyclic_subspace
Square matrix constructed from a monic polynomial
F n {\displaystyle A:F^{n}\to F^{n}} makes F n {\displaystyle F^{n}} a cyclic F [ A ] {\displaystyle F[A]} -module, having a basis of the form { v , A
Companion_matrix
Canonical form of matrices over a field
form reflects a minimal decomposition of the vector space into subspaces that are cyclic for A (i.e., spanned by some vector and its repeated images under
Frobenius_normal_form
Partially unsolved problem in mathematics
\{T^{n}(x)\,:\,n\geq 0\}} . This is also called the T {\displaystyle T} -cyclic subspace generated by x {\displaystyle x} . From the definition it follows that
Invariant_subspace_problem
In mathematics, vector subspace
linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when
Linear_subspace
Linear subspace generated from a vector acted on by a power series of a matrix
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 of b under
Krylov_subspace
Result about when a matrix can be diagonalized
\ldots } span a dense subspace of the Hilbert space. Suppose A {\displaystyle A} is a bounded self-adjoint operator for which a cyclic vector exists. In that
Spectral_theorem
Vector satisfying some of the criteria of an eigenvector
independent generalized eigenvectors which form a basis for an invariant subspace of V {\displaystyle V} . Using generalized eigenvectors, a set of linearly
Generalized_eigenvector
Von Neumann
In mathematics, the notion of a cyclic and separating vector is important in the theory of von Neumann algebras, and, in particular, in Tomita–Takesaki
Cyclic_and_separating_vector
mapping or Lorentz transformation Linear subspace Row and column spaces Column space Row space Cyclic subspace Null space, nullity Rank–nullity theorem
Outline_of_linear_algebra
The cyclic subspace Mh = {Mh : M ∈ M} is invariant under the action of any T in M. Its closure cl(Mh) in the norm of H is a closed linear subspace, with
Von Neumann bicommutant theorem
Von_Neumann_bicommutant_theorem
\theta \end{aligned}}} The non-trivial commutators used to identify the cyclic subspace for ( 1 ) → ( 2 ) {\displaystyle (1)\to (2)} are [ L y , 2 L z S z
Product_operator_formalism
Operator on a Hilbert space that shifts basis vectors
{D} } is not a cyclic vector. This is because every function in the span of its orbit will also be zero at that point, so the subspace cannot be dense
Unilateral_shift_operator
slipstream Vaadwaur subspace corridors (underspace) Xindi subspace vortex Borg transwarp conduits Wormholes geodesic fold intermittent cyclical vortex interspatial
Technology_in_Star_Trek
Correspondence in functional analysis
Gelfand–Naimark–Segal construction establishes a correspondence between cyclic ∗ {\displaystyle *} -representations of A {\displaystyle A} and certain
Gelfand–Naimark–Segal construction
Gelfand–Naimark–Segal_construction
In linear algebra, generated subspace
elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle V} that contains S . {\displaystyle S.} It is the set
Linear_span
Operation that combines groups
joined along a path-connected subspace, with F {\displaystyle F} taking the role of the fundamental group of the subspace. See: Seifert–van Kampen theorem
Free_product
Family of polynomials
coefficients, whose value when q is set to a prime power counts the number of subspaces of dimension k in a vector space of dimension n over F q {\displaystyle
Gaussian_binomial_coefficient
Type of mathematical generalization
transform, have been defined in this context. The Gaussian coefficients count subspaces of a finite vector space. Let q be the number of elements in a finite
Q-analog
Subset of a group that forms a group itself
These conditions alone imply that every element a of H generates a finite cyclic subgroup of H, say of order n, and then the inverse of a is an−1. If the
Subgroup
Type of vector space in mathematics
mathematics, the Lagrangian Grassmannian is the smooth manifold of Lagrangian subspaces of a real symplectic vector space V. Its dimension is 1/2n(n + 1) (where
Lagrangian_Grassmannian
Type of linear error-correcting code
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 elements
Binary_Golay_code
Concepts from linear algebra
distinct eigenvalues. Any subspace spanned by eigenvectors of T is an invariant subspace of T, and the restriction of T to such a subspace is diagonalizable.
Eigenvalues_and_eigenvectors
Certain topology in mathematics
on Z generates the subspace topology on Z, so that the subspace topology will not be an order topology even though it is the subspace topology of a space
Order_topology
Matrix representing a Euclidean rotation
space (or subspace). For a 2 × 2 matrix the trace is 2 cos θ, and for a 3 × 3 matrix it is 1 + 2 cos θ. In the three-dimensional case, the subspace consists
Rotation_matrix
Theorem in linear algebra
have non-trivial invariant coordinate subspaces. Here a non-trivial coordinate subspace means a linear subspace spanned by any nonempty proper subset
Perron–Frobenius_theorem
Numerical linear algebra algorithm
correctly account for the case in which one dimension is an independent subspace. For example, if given a diagonal matrix, the above implementation will
Jacobi_eigenvalue_algorithm
Type of group in mathematics
2), a line (in dimension 3), or in general around a (n-2)-dimensional subspace. In low dimension, these groups have been widely studied, see SO(2), SO(3)
Orthogonal_group
*-algebra of bounded operators on a Hilbert space
isomorphic to a subspace of another module if and only if it has smaller or equal M-dimension. A module is called standard if it has a cyclic separating vector
Von_Neumann_algebra
Mathematical representation
invariant subspace of H1(Dn) (under the action of Bn) is primitive and infinite cyclic. Let π : H1(Dn) → Z be the projection onto this invariant subspace. Then
Burau_representation
element s of GL(V) is called a pseudoreflection if it fixes a codimension 1 subspace of V and is not the identity transformation I, or equivalently, if the
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
Transformations induced by a mathematical group
Lie group and X {\displaystyle X} a differentiable manifold, then the subspace of smooth points for the action is the set of points x ∈ X {\displaystyle
Group_action
Mathematical theorem in representation theory
and G is the symmetric group S d {\displaystyle {\mathfrak {S}}_{d}} , a subspace of U {\displaystyle U} is a B-submodule if and only if it is invariant
Schur–Weyl_duality
Relation between sides of a right triangle
coordinate subspace. μ m p i {\displaystyle \mu _{mp_{i}}} is the measure of the m-dimensional set projection onto m-dimensional coordinate subspace i. Because
Pythagorean_theorem
Double cover Lie group of the special orthogonal group
\operatorname {Cl} ^{2}\oplus \operatorname {Cl} ^{4}\oplus \cdots } is the subspace generated by elements that are the product of an even number of vectors
Spin_group
133-dimensional exceptional simple Lie group
1/2,−1/2,−1/2,−1/2,−1/2) Note that the 7-dimensional subspace is the subspace where the sum of all the eight coordinates is zero. There are 126
E7_(mathematics)
Theoretical object in mathematics
{\frac {[n]!_{q}}{[m]!_{q}[n-m]!_{q}}}} gives the number of m-dimensional subspaces of an n-dimensional vector space over Fq. The expansion of the q‑binomial
Field_with_one_element
Gives the rank of the group of units in the ring of algebraic integers of a number field
{\textstyle N_{j}\log \left|u^{(j)}\right|} has an image in the r-dimensional subspace of R r + 1 {\displaystyle \mathbb {R} ^{r+1}} consisting of all vectors
Dirichlet's_unit_theorem
Upper bound on intersecting set families
apply to other kinds of mathematical object than sets, including linear subspaces, permutations, and strings. They again describe the largest possible intersecting
Erdős–Ko–Rado_theorem
Algebraic structure used in analysis
for groups) has analogs for Lie algebras. A Lie subalgebra is a linear subspace h ⊆ g {\displaystyle {\mathfrak {h}}\subseteq {\mathfrak {g}}} which is
Lie_algebra
Group of transformations under which the object is invariant
geometries preserve families of point-sets (discrete subspaces) rather than Euclidean subspaces, distances, or inner products. Just as for Euclidean figures
Symmetry_group
Process in quantum computing
and apply a unitary encoding circuit to rotate the global state into a subspace of a larger Hilbert space. This highly entangled, encoded state corrects
Quantum_error_correction
Automorphism group of a metric space or pseudo-Euclidean space
isometry group of the pseudo-Euclidean space. The isometry group of the subspace of a metric space consisting of the points of a scalene triangle is the
Isometry_group
Area of mathematics
whose coordinates sum to zero, and when n ≥ 2, the representation on this subspace is an (n − 1)-dimensional irreducible representation, called the standard
Representation theory of the symmetric group
Representation_theory_of_the_symmetric_group
On the approximate structure of sets whose sumset is small
^{-2}} . Generalizing this lemma to arbitrary cyclic groups requires an analogous notion to “subspace”: that of the Bohr set. Let R {\displaystyle R}
Freiman's_theorem
248-dimensional exceptional simple Lie group
grade operator within e 7 {\displaystyle {\mathfrak {e}}_{7}} ), each subspace may be given a quite particular non-associative (nor even power-associative)
E8_(mathematics)
Vector bundle existing over a Grassmannian
-dimensional subspaces of V {\displaystyle V} , given a point in the Grassmannian corresponding to a k {\displaystyle k} -dimensional vector subspace W ⊆ V {\displaystyle
Tautological_bundle
Non-abelian group of order eight
abelian subgroup is cyclic. It can be shown that a finite p-group with this property (every abelian subgroup is cyclic) is either cyclic or a generalized
Quaternion_group
Group homomorphism into the general linear group over a vector space
x 1 3 {\displaystyle x_{1}^{3}} to x 2 3 {\displaystyle x_{2}^{3}} . A subspace W of V that is invariant under the group action is called a subrepresentation
Group_representation
Type of group and algebra representation
G} -invariant subspaces, e.g. the whole vector space V {\displaystyle V} , and {0}). If there is a proper nontrivial invariant subspace, ρ {\displaystyle
Irreducible_representation
Homotopy invariant of maps between n-spheres
homotopy group π 3 ( S 2 ) {\displaystyle \pi _{3}(S^{2})} is the infinite cyclic group generated by η {\displaystyle \eta } . In 1951, Jean-Pierre Serre
Hopf_invariant
Mathematical connection between field theory and group theory
F ) {\displaystyle Der_{E}(F,F)\subset Der_{K}(F,F)} . Conversely, a subspace V ⊂ D e r K ( F , F ) {\displaystyle V\subset Der_{K}(F,F)} satisfying
Galois_theory
Relation between distances of four points
states that the inequality becomes an equality when the four points lie in cyclic order on a circle. The other case of equality occurs when the four points
Ptolemy's_inequality
Well studied projective geometries over finite fields
whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a partition is called a spread. Specifically
Spread_(projective_geometry)
Function in discrete mathematics
projection operator method does not produce orthogonal eigenvectors within one subspace. The operator P λ {\displaystyle {\mathcal {P}}_{\lambda }} can be seen
Discrete_Fourier_transform
Transformation in quantum mechanics
truncating their infinite-dimensional Fock space to finite-dimensional subspaces. One important aspect of quantum mechanics is the occurrence of—in general—non-commuting
Holstein–Primakoff transformation
Holstein–Primakoff_transformation
Concept in mathematics
{\mathfrak {g}}} . The subspace of g {\displaystyle {\mathfrak {g}}} corresponding to each root is 1-dimensional, and the subspace of g {\displaystyle {\mathfrak
Reductive_group
Geometric symmetry operation
reflection in a hyperplane ( n − 1 {\displaystyle n-1} dimensional affine subspace – a point on the line, a line in the plane, a plane in 3-space), with the
Point_reflection
Group of geometric symmetries with at least one fixed point
gives the four-dimensional reflection groups (excluding those that leave a subspace fixed and that are therefore lower-dimensional reflection groups). Each
Point_group
Concept in class field theory
does not have the subspace topology, but rather a finer topology. This topology is defined by giving the inertia subgroup its subspace topology and imposing
Weil_group
Elements taken to zero by a homomorphism
its kernel is reduced to the zero subspace. The kernel ker T {\displaystyle \ker {T}} is always a linear subspace of V {\displaystyle V} . Thus, it
Kernel_(algebra)
Periodic set of points
{\displaystyle \ell } -dimensional Q {\displaystyle \mathbb {Q} } -linear subspace V ⊂ Q n {\displaystyle V\subset \mathbb {Q} ^{n}} For every v ∈ Z n {\displaystyle
Lattice_(group)
Textbook by Ramamurti Shankar
Spaces: Basics Inner Product Spaces Dual Spaces and the Dirac Notation Subspaces Linear Operators Matrix Elements of Linear Operators Active and Passive
Principles of Quantum Mechanics
Principles_of_Quantum_Mechanics
Representations of finite groups, particularly on vector spaces
representation is faithful. The subspace C e 2 {\displaystyle \mathbb {C} e_{2}} is a D 6 {\displaystyle D_{6}} –invariant subspace. Thus, there exists a nontrivial
Representation theory of finite groups
Representation_theory_of_finite_groups
78-dimensional exceptional simple Lie group
(as a complex or compact Lie group) is the cyclic group Z/3Z, and its outer automorphism group is the cyclic group Z/2Z. For the simply-connected form
E6_(mathematics)
include: number of wanted eigenvalues, tolerance, size of the employed subspaces, part of the spectrum of interest. ST encapsulates spectral transformations
SLEPc
Axiomatization of quantum field theory
particular, the pure states are given by the rays, i.e. the one-dimensional subspaces, of some separable complex Hilbert space. In the following, the scalar
Wightman_axioms
16-element matrix group
spaces, a symplectic subspace corresponds to a direct sum of Pauli algebras (i.e., encoded qubits), while an isotropic subspace corresponds to a set of
Pauli_group
Geometric model of the physical space
exists. When relativity theory is considered, it can be considered a local subspace of space-time. While this space remains the most widely used way to model
Three-dimensional_space
Concept in quantum mechanics of perfectly substitutable particles
dimensional symmetric/bosonic subspace and anti-symmetric/fermionic subspace. There are however more types of irreducible subspaces. States associated with
Indistinguishable_particles
Monster and modular connection
involution lifting h. To get the Moonshine Module, one takes the fixed point subspace of h in the direct sum of VL and its twisted module. Frenkel, Lepowsky
Monstrous_moonshine
Polynomial associated with a matrix
distinct factors over such a field. This is a part of representation theory of cyclic groups. P = X 2 − X = X ( X − 1 ) {\displaystyle P=X^{2}-X=X(X-1)} : endomorphisms
Minimal polynomial (linear algebra)
Minimal_polynomial_(linear_algebra)
Topological space
specifically in topology, the Volodin space X {\displaystyle X} of a ring R is a subspace of the classifying space B G L ( R ) {\displaystyle BGL(R)} given by X
Volodin_space
Hypercomplex number system
. The set of all purely imaginary octonions spans a 7-dimensional subspace of O , {\displaystyle \mathbb {O} ,} denoted I m [ O ] {\displaystyle
Octonion
Abstract regular 4-polytope
abstract structure is geometric configuration (116) and can be defined with a cyclic configuration, with a generator "line" as {0,1,2,4,5,7}11. (Sequential lines
11-cell
Mathematical theorem
given the product topology, and End(DU) is viewed as a subspace of UU and is given the subspace topology, then R acts densely on U if and only if R is
Jacobson_density_theorem
Statement in abstract algebra
one-dimensional subspaces; the number of such factors is fixed, namely the dimension of the space, but there is a lot of freedom for choosing the subspaces themselves
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Nonparametric spectral estimation method
frequency domain decomposition. The origins of SSA and, more generally, of subspace-based methods for signal processing, go back to the eighteenth century
Singular_spectrum_analysis
finite group is a rational linear combination of characters induced from all cyclic subgroups of the group. There is a similar but in some sense more precise
Artin's theorem on induced characters
Artin's_theorem_on_induced_characters
Type of two-dimensional quasiparticle
corresponds to a linear transformation on this subspace of degenerate states. When there is no degeneracy, this subspace is one-dimensional and so all such linear
Anyon
Result on the topology of operators on an infinite-dimensional, complex Hilbert space
is the subgroup in which a given operator acts non-trivially only on a subspace spanned by the first N of a fixed orthonormal basis {ei}, for some N, being
Kuiper's_theorem
Branch of mathematics
famous theorem on the diagonals of a cyclic quadrilateral. Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalization of
Geometry
Identifies the commutant of a specific von Neumann algebra
conjugation operator. It is immediately verified that JMJ and M commute on the subspace M Ω, so that J M J ⊆ M ′ . {\displaystyle JMJ\subseteq M^{\prime }.} The
Commutation theorem for traces
Commutation_theorem_for_traces
Four-dimensional number system
is isomorphic to C {\displaystyle \mathbb {C} } , and is thus a planar subspace of H {\displaystyle \mathbb {H} } : write q as the sum of its scalar part
Quaternion
Optimization algorithm
studied, in the case when the sets C , D {\displaystyle C,D} were linear subspaces, by John von Neumann), which initializes x 0 = r {\displaystyle x_{0}=r}
Dykstra's projection algorithm
Dykstra's_projection_algorithm
X} , and D is the closure of the usual Dirac operator acting on a dense subspace of the Hilbert space Γ {\displaystyle \Gamma } of square integrable sections
Spectral_triple
Lie group of complex numbers of unit modulus; topologically a circle
abstract algebraic object. It has a natural topology when regarded as a subspace of the complex plane. It is a metric space with (at least) two natural
Circle_group
Type of topological group
group G is a discrete subgroup if H is discrete when endowed with the subspace topology from G. In other words there is a neighbourhood of the identity
Discrete_group
In algebra, integer associated to a module
the zero-dimensional intersection of the variety with a generic linear subspace of complementary dimension. More generally, the intersection multiplicity
Length_of_a_module
Matrix decomposition
M {\displaystyle \mathbf {M} } . By the rank–nullity theorem, these subspaces cannot have the same dimension if m ≠ n {\displaystyle m\neq n} . Even
Singular_value_decomposition
Mathematics award
Banach space contains either a subspace with many symmetries (technically, with an unconditional basis) or a subspace every operator on which is Fredholm
Fields_Medal
Order-preserving mathematical function
(possibly empty) set f − 1 ( y ) {\displaystyle f^{-1}(y)} is a connected subspace of X . {\displaystyle X.} In functional analysis on a topological vector
Monotonic_function
Non-commutative group with 6 elements
b\mid a^{2},b^{2},(ab)^{3}\rangle } where a and b are swaps and r = ab is a cyclic permutation. Note that the second presentation means that the group is a
Dihedral_group_of_order_6
Millennium Prize Problem
particular, the pure states are given by the rays, i.e. the one-dimensional subspaces, of some separable complex Hilbert space. The Wightman axioms require
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Five coplanar points have a subset forming a convex quadrilateral
projecting the higher-dimensional point set into an arbitrary two-dimensional subspace. However, the number of points necessary to find k points in convex position
Happy_ending_problem
Algebraic structure used in topology
cohomology groups H i ( X , Y ; A ) {\displaystyle H^{i}(X,Y;A)} for any subspace Y {\displaystyle Y} of a space X {\displaystyle X} . They are related to
Cohomology
Isometry group of Euclidean space
m-dimensional subspace combined with a discrete group of isometries in the orthogonal (n−m)-dimensional space one of these groups in an m-dimensional subspace combined
Euclidean_group
Algebraic structure
non-zero elements of a finite field form a multiplicative group. This group is cyclic, so all non-zero elements can be expressed as powers of a single element
Finite_field
Theorem in homotopy theory
theorem does not hold for general topological spaces or even for all subspaces of Rn. For example, the Warsaw circle, a compact subset of the plane,
Whitehead_theorem
{\displaystyle C[N]\rtimes G} in a similar way; this algebra is a sum of subspaces gC[N] as g runs through the elements of G, and is the group algebra of
Crossed_product
CYCLIC SUBSPACE
CYCLIC SUBSPACE
Boy/Male
English
royal.
Surname or Lastname
English
English : habitational name from a place in Cheshire named Kelsall, from the Middle English personal name Kell + Old English halh ‘nook or corner of land’, or possibly from Kelshall in Hertfordshire, which is named with an Old English personal name Cylli + Old English hyll ‘hill’, or even Kelsale in Suffolk, named with an Old English personal name Cēl(i) or Cēol + Old English halh.
Boy/Male
Tamil
Janardan | ஜநாரà¯à®¤à®¨
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Janardan | ஜநாரà¯à®¤à®¨
Boy/Male
Hindu
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Male
Spanish
Spanish name of Germanic origin, possibly GUIOMAR means "famous in battle." In the 13th century Vulgate Cycle of Arthurian romance, Sir Guiomar is the proud and beautiful knight of the crystal stream.
Boy/Male
Anglo, British, English
With Royal Might
Boy/Male
Tamil
Janardhan | ஜநாரà¯à®¤à®¨
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Janardhan | ஜநாரà¯à®¤à®¨
Boy/Male
Tamil
Janardana | ஜநாரà¯à®¤à®¨
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Janardana | ஜநாரà¯à®¤à®¨
Boy/Male
Hindu
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Girl/Female
American, Arabic, Australian, British, Chinese, English
Stone of the Colic; The Gemstone Jade; Green in Colour
Male
Irish
Irish name CAILTE means "the thin man." This is the name of a character from the Fenian cycle.
Surname or Lastname
English
English : nickname from Middle English loller ‘indolent fellow’, a derivative of lolle ‘to droop, dangle, or loll’.English : nickname from Middle English lollere ‘mumbler’, bestowed on a pious person or on a Lollard (a follower of the 14th-century religious reformer John Wyclif).
Boy/Male
Tamil
Janardhana | ஜநாரà¯à®¤à®¾à®¨à®¾
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Janardhana | ஜநாரà¯à®¤à®¾à®¨à®¾
Boy/Male
Hindu
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Boy/Male
Hindu
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Boy/Male
Hindu, Indian, Marathi
Vishnu; The Healer; Who Cures the Disease of Birth and Death Cycles
Boy/Male
Hindu
Free from the cycle of births and deaths
Boy/Male
Tamil
Jaramarana Varjita | ஜராமாஂரநா வரà¯à®œà¯€à®¤à®¾
Free from the cycle of births and deaths
Jaramarana Varjita | ஜராமாஂரநா வரà¯à®œà¯€à®¤à®¾
Girl/Female
Hindu, Indian, Traditional
The Periphery or Rim of a Wheel or Cycle
Boy/Male
Assamese, Hindu, Indian, Marathi
The Healer; Vishnu; Who Cures the Disease of Birth and Death Cycles
CYCLIC SUBSPACE
CYCLIC SUBSPACE
Male
Egyptian
, first king of Egypt; the son of Io.
Boy/Male
Greek
Golden mouthed.
Girl/Female
Biblical
Valley of sight.
Boy/Male
Latin
God of forests.
Girl/Female
Bengali, Indian
Durga
Boy/Male
Hindu, Indian
Addressing Jain God
Surname or Lastname
English
English : variant of Bolger.
Boy/Male
Muslim
Rare, Uncommon
Girl/Female
Tamil
Virangana | வீராஂகநா
Brave lady, Rani laxmibai
Girl/Female
American, Anglo, Australian, British, English
Ash Tree Settlement; Town of Ash Trees
CYCLIC SUBSPACE
CYCLIC SUBSPACE
CYCLIC SUBSPACE
CYCLIC SUBSPACE
CYCLIC SUBSPACE
n.
One entire round in a circle or a spire; as, a cycle or set of leaves.
imp. & p. p.
of Cycle
a.
Pertaining to the Dog Star; as, the cynic, or Sothic, year; cynic cycle.
n.
The act or practice of using a cycle; cycling.
a.
Alt. of Cyclical
p. pr. & vb. n.
of Cycle
n.
A mean or inferior poet, perhaps from his habit of wandering around as a stroller; an itinerant poet. Also, a name given to the cyclic poets. See under Cyclic, a.
a.
Containing cysts; cystose; as, cystic sarcoma.
n.
A cycler.
a.
Of or pertaining to a cycle or circle; moving in cycles; as, cyclical time.
a.
See Cystic.
n.
One who rides a bicycle or tricycle; a cycler, or cyclist.
a.
Having the form of, or living in, a cyst; as, the cystic entozoa.
a.
Of or pertaining to matter; material; corporeal; as, hylic influences.
a.
Of or pertaining to colic; affecting the bowels.
v. i.
To ride a bicycle, tricycle, or other form of cycle.
a.
Adhering to a fixed circle of legends; cyclic; hence, mean; inferior. See Cyclic poets, under Cyclic.
a.
Of or pertaining to the colon; as, the colic arteries.
v. i.
To pass through a cycle of changes; to recur in cycles.
n.
The act, art, or practice, of riding a cycle, esp. a bicycle or tricycle.