Block / Table / Rectangular Array
A matrix is an ordered rectangular array of numbers. A matrix with m rows and n columns has size m x n. The entry in the ith row and the jth column of a matrix A is denoted by a_{ij}.
Entries
Rows
Columns
Size = rows x columns
Definition
A matrix is an ordered rectangular array of numbers. A matrix with m rows and n columns has size m x n. The entry in the ith row and the jth column of a matrix A is denoted by a_{ij}.
Special Matrices
Row matrix
Column matrix
Square matrix
Two matrices are equal if they have the same size and their corresponding entries are equal.
If A is a matrix and c is a real number, then the scalar product cA is the matrix obtained by multiplying each entry of A by c.
If A is an m x n matrix with elements a_{ij}, then the transpose of A is the n x m matrix A^T with elements a_{ji}.
If A and B are two matrices of the same size, then:The sum A+B is the matrix obtained by adding the corresponding entries in the two matrices.the difference A-B is the matrix obtained by subtracting the corresponding entries in B from those in A.
Definitions
If A and B are two matrices of the same size, then:The sum A+B is the matrix obtained by adding the corresponding entries in the two matrices.the difference A-B is the matrix obtained by subtracting the corresponding entries in B from those in A.
Laws for Matrix Addition
If A, B, and C are matrices of the same size, thenA+B = B+A (commutative law)(A+B)+C = A+(B+C) (associative law)
Zero Matrix
A zero matrix is one in which all entries are zero.A zero matrix O has the property that A+O = O+A = A for any matrix A having the same size as that of O.