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In mathematics, a matrix ( pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " matrix ...
Matrix (protocol), an open standard for real-time communication. Matrix (record production), or master, a disc used in the production of phonograph records. Matrix number, of a gramophone record. Diode matrix, a two-dimensional grid of intersecting diodes. Display matrix, picture elements of an information display arranged as a matrix.
Block matrix. 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. [1] [2] Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or ...
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of 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 of rows of the ...
Elementary matrix. In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group GLn(F) when F is a field. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right ...
Miscellaneous. v. t. e. In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices ...
Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity matrix. [2] Over a field, a square matrix that is not invertible is called singular or degenerate. A square matrix with entries in a field is singular if and only if its determinant is zero.
Local extrema. A general quadratic form on real variables can always be written as where is the column vector with those variables, and is a symmetric real matrix. Therefore, the matrix being positive definite means that has a unique minimum (zero) when is zero, and is strictly positive for any other.