# Matrix

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.

3.Zero 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

Symmetric matrices

A square matrix is said to be symmetric if A1 = A.

Skew-Symmetric matrices

A square matrix A is said to be skew-symmetric if A1 = -A.

Determinants

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.

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