# Equal matrices

Two matrices are said to be equal if they have the same order and each element of one is equal to the corresponding element of the other.

# Row matrix

A matrix having a single row is called a row matrix, e.g., [1 3 5 7].

# Column matrix

A matrix having a single column is called a column matrix, e.g., .

# Square matrix

An m Ã— n matrix A is said to be a square matrix if m = n, i.e., number of rows = number of columns.

The diagonal from the left-hand side upper corner to the right-hand side lower corner is known as leading diagonal or principal diagonal.

# Diagonal matrix

A square matrix all of whose elements, except those in the leading diagonal, are zero is called a diagonal matrix. For a square matrix A = [aij]nÃ—n to be a diagonal matrix, aij = 0, whenever i â‰  j.

A diagonal matrix of order n Ã— n having d1, d2, ..., dn as diagonal elements is denoted by diag [d1, d2, ..., dn].

# Scalar matrix

A diagonal matrix whose all the leading diagonal elements are equal is called a scalar matrix.

For a square matrix A = [aij]n Ã— n to be a scalar matrix aij = , where m â‰  0.

# Unit matrix or identity matrix

A diagonal matrix of order n, which has unity for all its diagonal elements, is called a unit matrix of order n and is denoted by ln.

Thus, a square matrix A = [aij]n Ã— n is a unit matrix if aij = .

# Triangular matrix

A square matrix in which all the elements below the diagonal are zero is called upper triangular matrix and a square matrix in which all the elements above diagonal are zero is called lower triangular matrix.

Given a square matrix A = [aij]n Ã— n; for upper triangular matrix, aij = 0, i > j; and for lower triangular matrix, aij = 0, i < j.

# Null matrix

If all the elements of a matrix (square or rectangular) are zero, it is called a null or zero matrix.

For A = [aij] to be null matrix, aij = 0 âˆ€ i, j.

# Singular and non-singular matrix

A square matrix A is said to be non-singular if |A| â‰  0, and a square matrix A is said to be singular if |A| = 0.