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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., 63348.png.

Square matrix

An m × 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]n×n to be a diagonal matrix, aij = 0, whenever ij.
 
A diagonal matrix of order n × 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 × n to be a scalar matrix aij = 63342.png, where m ≠ 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 × n is a unit matrix if aij = 63329.png.

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 × 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 i, j.

Singular and non-singular matrix

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




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