mathematics, the spectrum of a matrix is the set of its eigenvalues. More generally, if T : V → V {\displaystyle T\colon V\to V} is a linear operator on...

autism spectrum describes a range of conditions classified as neurodevelopmental disorders. In mathematics, the spectrum of a matrix is the multiset of the...

algebra, the prime spectrum (or simply the spectrum) of a commutative ring R {\displaystyle R} is the set of all prime ideals of R {\displaystyle R}...

conjugate pairs. The spectrum of a matrix is the list of eigenvalues, repeated according to multiplicity; in an alternative notation the set of eigenvalues with...

field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation...

mathematics, spectrum frequently denotes a set of numbers associated to an object: Spectrum of a matrix, its set of eigenvalues, in linear algebra Spectrum (functional...

the adjacency matrix of the complement of G. The multiset of eigenvalues of this matrix is called the Seidel spectrum. The Seidel matrix was introduced...

mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization...

spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator...

science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent...

physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability...

range of the Rayleigh quotient (for any matrix, not necessarily Hermitian) is called a numerical range and contains its spectrum. When the matrix is Hermitian...

statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving...

A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links...

integers. While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory...

Proposition—A normal matrix is unitary if and only if all of its eigenvalues (its spectrum) lie on the unit circle of the complex plane. Proposition—A normal...

Because the characteristic polynomial of a product of two matrices is independent of the order, the spectrum of a matrix product is invariant under cyclic...

eigenvalues of a linear endomorphism are invariant under a change of basis. In other words, the spectrum of a matrix is invariant under a change of basis....

field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix...

matrix theory, the spread of a matrix is the largest distance in the complex plane between any two eigenvalues of the matrix. Let A {\displaystyle A}...

eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only...

the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities are...

density for microparticles standard deviation of a random variable in statistics Spectrum of a matrix Spin τ {\displaystyle \tau } represents: torque...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...

In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of the form: A X + X B = C . {\displaystyle AX+XB=C.} It is...

eigenvalues of a real square matrix A are complex numbers that make up the spectrum of the matrix. The exponential growth rate of the matrix powers Ak as...

time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis...

the spectrum of a C*-algebra or dual of a C*-algebra A, denoted Â, is the set of unitary equivalence classes of irreducible *-representations of A. A *-representation...

ranges over the spectrum of A {\displaystyle A} . When the matrix being decomposed is Hermitian, the spectral decomposition is a special case of the Schur decomposition...

In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is...