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Table of Contents Math Background Matrices Fundamentals | |
See also: data matrix, matrix algebra, Generalized Mean |
The following are a few basic definitions concerning matrices.
Definition. A matrix is a rectangularly shaped array with m rows and n columns of mn mathematical objects of a given basic set. The order of a matrix is mn ("m by n"). Each column and each row of a matrix defines a vector. A column vector is nothing other than an m1 matrix, and a row vector is a 1n matrix.
Matrices are denoted by bold uppercase letters, e.g. A.
Matrix elements are denoted by lowercase letters subscripted by two indices,
i.e. a_{m,n}. Sometimes the comma between the indices is omitted.
The sequence of the indices is not arbitrary; the first index always denotes
the row, the second index the column. If m=n, the matrix is called a square
matrix of order n. If a matrix is square, the diagonal containing elements
of equal indices (a_{11}, a_{22}, ..., a_{nn})
is called the principal diagonal of this matrix. The trace
of a matrix is the sum of all elements of the principal diagonal.
Last Update: 2006-Jän-17