In mathematics, a nonnegative matrix, written X ≥ 0 , {\displaystyle \mathbf {X} \geq 0,} is a matrix in which all the elements are equal to or greater...

Web-scale data mining, e.g., see Distributed Nonnegative Matrix Factorization (DNMF), Scalable Nonnegative Matrix Factorization (ScalableNMF), Distributed...

mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing...

positive or zero (that is, nonnegative). Negative-definite and negative semi-definite matrices are defined analogously. A matrix that is not positive semi-definite...

In mathematics, a Metzler matrix is a matrix in which all the off-diagonal components are nonnegative (equal to or greater than zero): ∀ i ≠ j x i j ≥...

algebra, a square nonnegative matrix A {\displaystyle A} of order n {\displaystyle n} is said to be productive, or to be a Leontief matrix, if there exists...

In linear algebra, the nonnegative rank of a nonnegative matrix is a concept similar to the usual linear rank of a real matrix, but adding the requirement...

eiH, where e indicates the matrix exponential, i is the imaginary unit, and H is a Hermitian matrix. For any nonnegative integer n, the set of all n × n...

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

solution. Any P-matrix is a Q-matrix. Conversely, if a matrix is a Z-matrix and a Q-matrix, then it is also a P-matrix. P-matrix Z-matrix Karamardian, S...

an M-matrix is a matrix whose off-diagonal entries are less than or equal to zero (i.e., it is a Z-matrix) and whose eigenvalues have nonnegative real...

complex, symmetric matrix A. Decomposition: A = V D V T {\displaystyle A=VDV^{\mathsf {T}}} , where D is a real nonnegative diagonal matrix, and V is unitary...

eigenvectors are generally different if AB ≠ BA. One may raise a square matrix to any nonnegative integer power multiplying it by itself repeatedly in the same...

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

linear algebra, a real symmetric matrix A is copositive if x ⊤ A x ≥ 0 {\displaystyle x^{\top }Ax\geq 0} for every nonnegative vector x ≥ 0 {\displaystyle...

Laplacian is a symmetric matrix if and only if the adjacency matrix A is symmetric and the diagonal entries of D are nonnegative, in which case we can use...

{\displaystyle c} as a nonnegative real number) and an exponential function c e x {\displaystyle ce^{x}} ( c {\displaystyle c} as a nonnegative real number). Convex...

doubly stochastic matrix (also called bistochastic matrix) is a square matrix X = ( x i j ) {\displaystyle X=(x_{ij})} of nonnegative real numbers, each...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

3847/1538-4357/aaa1f2. S2CID 3966513. Zhu, Guangtun B. (2016-12-19). "Nonnegative Matrix Factorization (NMF) with Heteroscedastic Uncertainties and Missing...

assume that A is an m × n matrix, and we define the linear map f by f(x) = Ax as above. The rank of an m × n matrix is a nonnegative integer and cannot be...

PMID 10548103. Wang, Hua; Nie, Feiping; Huang, Heng; Ding, Chris (2011). "Nonnegative Matrix Tri-factorization Based High-Order Co-clustering and Its Fast Implementation"...

0.CO;2-L. Lin, Chih-Jen (2007). "Projected Gradient Methods for Nonnegative Matrix Factorization" (PDF). Neural Computation. 19 (10): 2756–2779. CiteSeerX 10...

Guan, Naiyang; Tao, Dacheng; Luo, Zhigang; Yuan, Bo (2012). "Online nonnegative matrix factorization with robust stochastic approximation". IEEE Transactions...

doi:10.1086/510127. S2CID 18561804. Zhu, Guangtun B. (2016-12-19). "Nonnegative Matrix Factorization (NMF) with Heteroscedastic Uncertainties and Missing...

problem A − λ I q = 0, where the nonnegative matrix A must be square and where the diagonal matrix I is the identity matrix. Von Neumann's irreducibility...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

nonnegative n-square matrix is the graph with vertices numbered 1, ..., n and arc ij if and only if Aij ≠ 0. If the underlying graph of such a matrix...

or information-theoretic sense. A second approach, exemplified by nonnegative matrix factorization, is to impose structural constraints on the source signals...

abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set...