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What (who) is Z-matrix (mathematics) - definition

SQUARE MATRIX WHOSE OFF-DIAGONAL ENTRIES ARE NONPOSITIVE

Stoquastic

Z-matrix (mathematics)

In mathematics, the class of Z-matrices are those matrices whose off-diagonal entries are less than or equal to zero; that is, the matrices of the form:

https://en.wikipedia.org/wiki/Z-matrix_(mathematics)

MATRIX MATH

$An undirected graph with adjacency matrix: <math display="block">\begin{bmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}.</math>$
$Two different Markov chains. The chart depicts the number of particles (of a total of 1000) in state "2". Both limiting values can be determined from the transition matrices, which are given by <math> \begin{bmatrix} 0.7 & 0\\ 0.3 & 1 \end{bmatrix}</math> (red) and <math> \begin{bmatrix} 0.7 & 0.2\\ 0.3 & 0.8 \end{bmatrix}</math> (black).$

RECTANGULAR ARRAY OF NUMBERS, SYMBOLS, OR EXPRESSIONS, ARRANGED IN ROWS AND COLUMNS

Matrix (Mathematics); Matrix (math); Submatrix; Matrix theory; Matrix (maths); Submatrices; Matrix Theory and Linear Algebra; Infinite matrix; Square (matrix); Matrix operation; Square submatrix; Matrix(mathematics); Real matrix; Matrix math; Matrix index; Equal matrix; Matrix equation; Matrix (computer science); Matrix notation; Empty matrix; Real matrices; Principal submatrix; Array (mathematics); Matrix power; Complex matrix; Complex matrices; Applications of matrices; Rectangular matrix; Uniform matrix

<language> An early system on the UNIVAC I or II. [Listed in CACM 2(5):1959-05-16]. (1997-02-27)

Logical matrix

MATRIX WITH ENTRIES FROM THE BOOLEAN DOMAIN B = {0, 1}

Binary matrix; (0,1) matrix; (0,1)-matrix; (0,1)-matrices; 0,1-matrix; 0-1 matrix; Matrix logic; Zero-One matrix; Logical vector; Logical matrices

A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets.

https://en.wikipedia.org/wiki/Logical_matrix

Wikipedia

Z-matrix (mathematics)

In mathematics, the class of Z-matrices are those matrices whose off-diagonal entries are less than or equal to zero; that is, the matrices of the form:

Z=(z_{ij});\quad z_{ij}\leq 0,\quad i\neq j.

Note that this definition coincides precisely with that of a negated Metzler matrix or quasipositive matrix, thus the term quasinegative matrix appears from time to time in the literature, though this is rare and usually only in contexts where references to quasipositive matrices are made.

The Jacobian of a competitive dynamical system is a Z-matrix by definition. Likewise, if the Jacobian of a cooperative dynamical system is J, then (−J) is a Z-matrix.

Related classes are L-matrices, M-matrices, P-matrices, Hurwitz matrices and Metzler matrices. L-matrices have the additional property that all diagonal entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a Z-matrix is an M-matrix if it is nonsingular and its inverse is nonnegative. All matrices that are both Z-matrices and P-matrices are nonsingular M-matrices.

In the context of quantum complexity theory, these are referred to as stoquastic operators.

https://en.wikipedia.org/wiki/Z-matrix (mathematics)