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space H has a cyclic vector f if the vectors f, Af, A2f,... span H. Equivalently, f is a cyclic vector for A in case the set of all vectors of the form
Cyclic_vector
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
functional analysis, a cyclic subspace is a certain special subspace of a vector space associated with a vector in the vector space and a linear transformation
Cyclic_subspace
Result about when a matrix can be diagonalized
\lambda \mapsto \lambda } . A vector φ {\displaystyle \varphi } is called a cyclic vector for A {\displaystyle A} if the vectors φ , A φ , A 2 φ , … {\displaystyle
Spectral_theorem
Operator on a Hilbert space that shifts basis vectors
}|f(z)|=0} , may or may not be cyclic. For example, f ( z ) = 1 − z {\displaystyle f(z)=1-z} is a cyclic vector. The cyclic vectors are precisely the outer functions
Unilateral_shift_operator
Correspondence in functional analysis
called a cyclic representation. Any non-zero vector of an irreducible representation is cyclic. However, non-zero vectors in a general cyclic representation
Gelfand–Naimark–Segal construction
Gelfand–Naimark–Segal_construction
Partially unsolved problem in mathematics
for which every non-zero vector x ∈ H {\displaystyle x\in H} is a cyclic vector for T {\displaystyle T} . (Where a "cyclic vector" x {\displaystyle x} for
Invariant_subspace_problem
Type of block code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting
Cyclic_code
Theorem in axiomatic quantum field theory
that the vacuum state | Ω ⟩ {\displaystyle \vert \Omega \rangle } is a cyclic vector for the field algebra A ( O ) {\displaystyle {\mathcal {A}}({\mathcal
Reeh–Schlieder_theorem
Indian academic (1946–2019)
and received a PhD in Reproducing Kernels and Operators with a Cyclic Vector (Cycle Vector Space Theory) in 1969 under doctoral advisor John L. Kelley.
Vashishtha_Narayan_Singh
Mathematics theorem in functional analysis
non-negative z in A and f(−x* x) < 0. Consider the GNS representation πf with cyclic vector ξ. Since ‖ π f ( x ) ξ ‖ 2 = ⟨ π f ( x ) ξ ∣ π f ( x ) ξ ⟩ = ⟨ ξ ∣ π
Gelfand–Naimark_theorem
Mathematical operation on vectors in 3D space
is that they can be deduced from any other of them by a cyclic permutation of the basis vectors. This mnemonic applies also to many formulas given in this
Cross_product
Families of matrices in mathematics, physics, and quantum information
the shift matrix is just the translation operator (a cyclic permutation matrix) in that cyclic vector space, so the exponential of the momentum. They are
Generalizations of Pauli matrices
Generalizations_of_Pauli_matrices
Canonical form of matrices over a field
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 A). Since
Frobenius_normal_form
Circulation density in a vector field
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional
Curl_(mathematics)
R-module which is also a finite-dimensional vector space over F, then the Jordan blocks of x acting on V are cyclic submodules. (The Jordan blocks are all
Cyclic_module
Definite integral of a scalar or vector field along a path
referred to in engineering as a cyclic integral. To establish a complete analogy with the line integral of a vector field, one must go back to the definition
Line_integral
Alternative mathematical ordering
In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order is not modeled
Cyclic_order
Set of a ring's prime ideals
corresponds to a reduced variety; a cyclic module (one generator) corresponds to the operator having a cyclic vector (a vector whose orbit under T spans the
Spectrum_of_a_ring
of Type III factors. According to Tomita–Takesaki theory, every vector which is cyclic for the factor and its commutant gives rise to a 1-parameter modular
Crossed_product
Commutative group in which all nonzero elements have the same order
non-negative integer (sometimes called the group's rank). Here, Z/pZ denotes the cyclic group of order p (or equivalently the integers mod p), and the superscript
Elementary_abelian_group
Representation of a tensor in Euclidean space
permutations in perpendicular directions yield the next vector in the cyclic collection of vectors: e x × e y = e z e y × e z = e x e z × e x = e y e y ×
Cartesian_tensor
Commutative group (mathematics)
underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler
Abelian_group
Concepts from linear algebra
algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear
Eigenvalues_and_eigenvectors
Four-dimensional number system
Quaternions can be used to represent vectors in three-dimensional space, which provides a definition of the quotient of two vectors. Quaternions were first described
Quaternion
matrix identity Vector space Linear combination Linear span Linear independence Scalar multiplication Basis Change of basis Hamel basis Cyclic decomposition
Outline_of_linear_algebra
M ) {\displaystyle L^{2}(M)} acted on by M {\displaystyle M} with a cyclic vector Ω {\displaystyle \Omega } . Let e N {\displaystyle e_{N}} be the projection
Subfactor
Vector used in astronomy
corresponding cyclic coordinate in the three-dimensional Lagrangian of the system, there does not exist such a coordinate for the LRL vector. Thus, the conservation
Laplace–Runge–Lenz_vector
Mathematics concept
In mathematics, cyclical monotonicity is a generalization of the notion of monotonicity to the case of vector-valued function. Let ⟨ ⋅ , ⋅ ⟩ {\displaystyle
Cyclical_monotonicity
Formulation of classical mechanics
point particles with masses m1, m2, ..., mN, each particle has a position vector, denoted r1, r2, ..., rN. Cartesian coordinates are often sufficient, so
Lagrangian_mechanics
Part of spectral theory
{\displaystyle (T^{n}\xi )} is dense in H, i.e. ξ {\displaystyle \xi } is a cyclic vector for T {\displaystyle T} , then the map U {\displaystyle U} defined by
Spectral theory of ordinary differential equations
Spectral_theory_of_ordinary_differential_equations
In linear algebra, generated subspace
linear hull or just span) of a set S {\displaystyle S} of elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle
Linear_span
Open convex self-dual cones
be the restriction of L(a) to E0. T is self-adjoint and has 1 as a cyclic vector. So the commutant of T consists of polynomials in T (or a). By the spectral
Symmetric_cone
Case in parallel computing
than the vector size. So, if the vector register is 128 bits, and the array type is 32 bits, the vector size is 128/32 = 4. All other non-cyclic dependencies
Automatic_vectorization
Parameterization of a rotation into a unit vector and angle
rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation
Axis–angle_representation
Four-sided polygon
to an inscribed circle. Cyclic quadrilateral: the four vertices lie on a circumscribed circle. A convex quadrilateral is cyclic if and only if opposite
Quadrilateral
{\displaystyle (\pi ,V)} of a Banach algebra A {\displaystyle A} , a cyclic vector is a vector v ∈ V {\displaystyle v\in V} such that π ( A ) v {\displaystyle
Glossary of functional analysis
Glossary_of_functional_analysis
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
Computational problem used in cryptography
x_{n-1})} Micciancio introduced cyclic lattices in his work in generalizing the compact knapsack problem to arbitrary rings. A cyclic lattice is a lattice that
Short integer solution problem
Short_integer_solution_problem
Algorithms and methods of plotting the Mandelbrot set on a computing device
subtract from n is in the interval [0, 1). For the coloring we must have a cyclic scale of colors (constructed mathematically, for instance) and containing
Plotting algorithms for the Mandelbrot set
Plotting_algorithms_for_the_Mandelbrot_set
Well-quasi-ordering of finite trees
theory Topics Glossary Category Key concepts Binary relation Boolean algebra Cyclic order Lattice Partial order Preorder Total order Weak ordering Results Boolean
Kruskal's_tree_theorem
Linear algebra matrix
n-1} . (Cyclic permutation of rows has the same effect as cyclic permutation of columns.) The last row of C {\displaystyle C} is the vector c {\displaystyle
Circulant_matrix
Matrices important in quantum mechanics and the study of spin
0 {\displaystyle \sigma _{0}} ), the Pauli matrices form a basis of the vector space of 2 × 2 {\displaystyle 2\times 2} Hermitian matrices over the real
Pauli_matrices
Symmetry of molecules of chemical compounds
turn divided into cyclic and dihedral groups and within a system the order of the dihedral group is twice that of the cyclic group. Cyclic groups only have
Molecular_symmetry
Generalization of vector spaces from fields to rings
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)
Module_(mathematics)
Gallrado-Gutiérez, Eva A.; Partington, Jonathan R.; Segura, Dolores (2009), Cyclic vectors and invariant subspaces for Bergman and Dirichlet shifts (PDF), vol
Bergman_space
American mathematician (born 1967)
completed her doctorate at Kent State in 1996; her dissertation, Cyclic Vectors and Extremal Vectors of Linear Operators, was supervised by Per Enflo. She was
Angela_Spalsbury
In mathematics, vector subspace
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 simply
Linear_subspace
Branch of mathematics
K-theory and K-homology provide analogues of vector bundles and elliptic operators. Cyclic homology and cyclic cohomology provide noncommutative analogues
Noncommutative_geometry
Partially ordered vector space, ordered as a lattice
mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice
Riesz_space
Correspondence between quaternions and 3D rotations
whose vector part is p, and then performing the quaternion conjugation. The vector part of the resulting pure quaternion is the desired vector r. Clearly
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Vector space with a partial order
ordered vector space or partially ordered vector space is a real vector space equipped with a partial order that is compatible with the vector space operations
Ordered_vector_space
Random variable with multiple component dimensions
probability and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either
Multivariate_random_variable
Algebraic object with an ordered structure
of redirect targets Ordered ring Ordered topological vector space Ordered vector space – Vector space with a partial order Partially ordered ring – Ring
Ordered_field
Antisymmetric permutation object acting on tensors
permutation, and 0 if any index is repeated. In three dimensions only, the cyclic permutations of (1, 2, 3) are all even permutations, similarly the anticyclic
Levi-Civita_symbol
Geometric transformation combining reflection and translation
reflection is an infinite cyclic group. Combining two equal glide reflections gives a pure translation with a translation vector that is twice that of the
Glide_reflection
Matrix representing a Euclidean rotation
with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: R v = [ cos θ − sin θ sin θ cos
Rotation_matrix
Group that is also a differentiable manifold with group operations that are smooth
acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket
Lie_group
In mathematics, the upper bound theorem states that cyclic polytopes have the largest possible number of faces among all convex polytopes with a given
Upper_bound_theorem
Type of group in mathematics
(whereas SO(n) is not abelian when n > 2). Its finite subgroups are the cyclic group Ck of k-fold rotations, for every positive integer k. All these groups
Orthogonal_group
Mathematical concept named for Ernst Witt
Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in such
Witt_vector
Circle that passes through the vertices of a triangle
also called the circumscribed circle, is called a cyclic polygon, or in the special case n = 4, a cyclic quadrilateral. All triangles, rectangles, isosceles
Circumcircle
Russian mathematician (born 1940)
jfa.2008.05.011. Nikolski, Nikolai (2012). "In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc". Annales de l'Institut Fourier
Nikolai_Kapitonovich_Nikolski
Norm on a vector space of matrices
mathematics, a norm in general is a function from a vector space to non-negative numbers. When the vector space comprises matrices, such norms are referred
Matrix_norm
Fundamental theorem in condensed matter physics
same periodicity as the crystal, the wave vector k {\displaystyle \mathbf {k} } is the crystal momentum vector, e {\displaystyle e} is Euler's number, and
Bloch's_theorem
Order-preserving mathematical function
coefficient - measure of monotonicity in a set of data Total monotonicity Cyclical monotonicity Operator monotone function Monotone set function Absolutely
Monotonic_function
states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated by pseudoreflections
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one
List_of_finite_simple_groups
Representation theory of groups
regular representation λ (over a field K) is a linear representation on the K-vector space V freely generated by the elements of G, i.e. elements of G can be
Regular_representation
Polyhedron with 20 faces
coordinates of the 12 vertices can be defined by the vectors defined by all the possible cyclic permutations and sign-flips of coordinates of the form
Icosahedron
topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order ≤ making it into an ordered vector space
Ordered topological vector space
Ordered_topological_vector_space
Special subset of a partially ordered set
lattice of vector subspaces of a given vector space, ordered by inclusion. Explicitly, a linear filter on a vector space X is a family B of vector subspaces
Filter_(mathematics)
Family of linear transformations
taking cyclic permutations of x, y, z components (i.e. change x to y, y to z, and z to x, repeat). These commutation relations, and the vector space of
Lorentz_transformation
V=\mathbb {C} (X)} be the vector space over the complex numbers with a basis indexed by a finite set X {\displaystyle X} . If the cyclic group C n {\displaystyle
Cyclic_sieving
Specialized notation for multivariable calculus
respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be
Matrix_calculus
Transformations induced by a mathematical group
polyhedron. A group action on a vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify
Group_action
Geometry concept
groups, except for C2 and D1, which share abstract group Z2. All of the cyclic groups are abelian or commutative, but only two of the dihedral groups are:
Point groups in two dimensions
Point_groups_in_two_dimensions
Method of encoding digital data on multiple carrier frequencies
which suffers from poor power efficiency Loss of efficiency caused by cyclic prefix/guard interval In OFDM, the subcarrier frequencies are chosen so
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Geometric model of the physical space
correspond to (the negative of) the scalar part and the vector part of the product of two vector quaternions. It was not until Josiah Willard Gibbs that
Three-dimensional_space
Vector bundle existing over a Grassmannian
In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k {\displaystyle
Tautological_bundle
topics on mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation
List_of_permutation_topics
Vector satisfying some of the criteria of an eigenvector
eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria which are more relaxed than those for an
Generalized_eigenvector
Abelian group related to division algebras
containing all roots of unity. The Brauer group BrR of the real numbers is the cyclic group of order two. There are just two non-isomorphic real division algebras
Brauer_group
Group in which the order of every element is a power of p
acting on symplectic vector spaces. Richard Brauer classified all groups whose Sylow 2-subgroups are the direct product of two cyclic groups of order 4,
P-group
Stock market valuation measure
The cyclically adjusted price-to-earnings ratio (CAPE, Shiller P/E, or P/E 10 ratio) is a stock valuation measure usually applied to the US S&P 500 equity
Cyclically adjusted price-to-earnings ratio
Cyclically_adjusted_price-to-earnings_ratio
Sum of elements on the main diagonal
can define the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect
Trace_(linear_algebra)
Mathematical object
ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts of number theory
Ideal_lattice
On chains and antichains in partial orders
theory Topics Glossary Category Key concepts Binary relation Boolean algebra Cyclic order Lattice Partial order Preorder Total order Weak ordering Results Boolean
Dilworth's_theorem
Group of transformations under which the object is invariant
function of position with values in a set of colors or substances; as a vector field; or as a more general function on the object.) The group of isometries
Symmetry_group
Type of infinitesimal in calculus
without a hole within it), then any irrotational vector field (defined as a C 1 {\displaystyle C^{1}} vector field v {\displaystyle \mathbf {v} } which curl
Exact_differential
Set with associative invertible operation
so these groups are cyclic. Indeed, each element is expressible as a sum all of whose terms are 1 {\displaystyle 1} . Any cyclic group with n {\displaystyle
Group_(mathematics)
Simple Lie group; the automorphism group of the octonions
equivalently, as the subgroup of SO(7) that preserves any chosen particular vector in its 8-dimensional real spinor representation (a spin representation)
G2_(mathematics)
Special type of lattice
is a Boolean algebra if and only if n is square-free. A lattice-ordered vector space is a distributive lattice. Young's lattice given by the inclusion
Distributive_lattice
Concept in mathematics
reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that
Complex_reflection_group
Type of rotorcraft
commonly called the cyclic stick or just cyclic or stick and moves forwards and backwards and side to side. On most helicopters, the cyclic is similar to a
Helicopter
Type of mathematical generalization
(e2πi/n)d be the d-th power of a primitive n-th root of unity. Let C be a cyclic group of order n generated by an element c. Let X be the set of k-element
Q-analog
Overview of mechanics based on the least action principle
considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system; it can also be called vectorial mechanics
Analytical_mechanics
Operation in mathematical calculus
curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes
Integral
Subset of a preorder that contains all larger elements
theory Topics Glossary Category Key concepts Binary relation Boolean algebra Cyclic order Lattice Partial order Preorder Total order Weak ordering Results Boolean
Upper_and_lower_sets
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
CYCLIC VECTOR
CYCLIC VECTOR
Girl/Female
Hindu, Indian, Traditional
The Periphery or Rim of a Wheel or Cycle
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
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
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
Hindu
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
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
Boy/Male
Hindu
Free from the cycle of births and deaths
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
Male
Irish
Irish name CAILTE means "the thin man." This is the name of a character from the Fenian cycle.
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
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.
Girl/Female
American, Arabic, Australian, British, Chinese, English
Stone of the Colic; The Gemstone Jade; Green in Colour
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, Indian, Marathi
Vishnu; The Healer; Who Cures the Disease of Birth and Death Cycles
Boy/Male
Hindu
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
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
Assamese, Hindu, Indian, Marathi
The Healer; Vishnu; Who Cures the Disease of Birth and Death Cycles
Boy/Male
Anglo, British, English
With Royal Might
CYCLIC VECTOR
CYCLIC VECTOR
Girl/Female
Indian
Beauty
Girl/Female
Tamil
Joshmitha | ஜோஷà¯à®®à¯€à®¤à®¾
Boy/Male
Australian, Danish, French, German, Swedish, Swiss
Leader of the People; People's Ruler; King of Nations
Girl/Female
Tamil
Wise
Boy/Male
Hindu
Pure or holy
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Oriya, Tamil, Telugu, Traditional
Lord of Mount Badri; Lord Vishnu; Lord Shiva
Boy/Male
Australian, Portuguese
White; Blond; Fair-one
Boy/Male
Tamil
King
Boy/Male
Hindu, Indian
Happy
Boy/Male
Muslim
A companion of prophet Muhammad
CYCLIC VECTOR
CYCLIC VECTOR
CYCLIC VECTOR
CYCLIC VECTOR
CYCLIC VECTOR
a.
Of or pertaining to a cycle or circle; moving in cycles; as, cyclical time.
a.
Of or pertaining to colic; affecting the bowels.
imp. & p. p.
of Cycle
n.
The act or practice of using a cycle; cycling.
n.
A cycler.
n.
One who rides a bicycle or tricycle; a cycler, or cyclist.
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.
n.
The act, art, or practice, of riding a cycle, esp. a bicycle or tricycle.
a.
Containing cysts; cystose; as, cystic sarcoma.
a.
Alt. of Cyclical
a.
Of or pertaining to matter; material; corporeal; as, hylic influences.
v. i.
To pass through a cycle of changes; to recur in cycles.
a.
Adhering to a fixed circle of legends; cyclic; hence, mean; inferior. See Cyclic poets, under Cyclic.
n.
One entire round in a circle or a spire; as, a cycle or set of leaves.
a.
Having the form of, or living in, a cyst; as, the cystic entozoa.
a.
See Cystic.
a.
Pertaining to the Dog Star; as, the cynic, or Sothic, year; cynic cycle.
p. pr. & vb. n.
of Cycle
v. i.
To ride a bicycle, tricycle, or other form of cycle.
a.
Of or pertaining to the colon; as, the colic arteries.