A matrix is a rectangular array of numbers arranged into rows and columns.
Types of Matrices
1. Row matrix
A matrix having one row and any number of columns is a row matrix
E.g.: A = [a b c d]1xn
2. Column matrix
A matrix having one column and any number of rows is known as column matrix.
A zero or null matrix is one whose elements are zeroes.
4. Square matrix
A matrix having same number of rows and columns is known as a square matrix.
5. Diagonal matrix
A square matrix having non-zero entries only on the main diagonal is known as diagonal matrix.
6. Scalar matrix
A diagonal matrix with equal non-zero entries on the same diagonal is known as scalar matrix.
7. Unit matrix (Identity matrix)
A diagonal matrix is a unit matrix each of the diagonal elements is unity.
Transpose of a matrix
The transpose of a matrix A is the matrix obtained by interchanging the rows and columns of A, and is denoted by A1 or AT.
(A1)1 = A
(A+B)1 = A1 + B1
(AB)1 = B1A1
(kA)1 = kA1, where k is a complex number
A square matrix is said to be symmetric if A1 = A.
A square matrix A is said to be skew-symmetric if A1 = -A.
To each square matrix A = [aij] we associate a number called determinant of A and is denoted by |A|. Matrices which are not square do not have determinants.
Singular and non-Singular matrices
A square matrix A is called singular if |A| = 0. If |A| ¹ 0 then A is called non-singular.