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matrices with the same number of rows and columns, play a major role in matrix theory. Square matrices of a given dimension form a noncommutative ring, which...

S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics. It avoided the notion of...

In theoretical physics, the matrix theory is a quantum mechanical model proposed in 1997 by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind;...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries...

In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising...

supergravity at low energies. Modern attempts to formulate M-theory are typically based on matrix theory or the AdS/CFT correspondence. According to Witten, M...

some aspects of matrix models and M-theory are described by a noncommutative quantum field theory, a special kind of physical theory in which spacetime...

physics, cosmology, and pure mathematics. String theory represents an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in...

n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or rarely regular) if there exists an n-by-n square matrix B such that A...

In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns...

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...

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

columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...

variations; see below. Incidence matrix is a common graph representation in graph theory. It is different to an adjacency matrix, which encodes the relation...

In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices...

Matrix model may refer to: a model using a matrix in mathematics Matrix theory (physics), a quantum mechanical model Matrix population models, a type...

for matrix multiplication? (more unsolved problems in computer science) In theoretical computer science, the computational complexity of matrix multiplication...

In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column...

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...