Different Types of Matrices – Definitions and Examples

Here you will what is matrix and definitions of different types of matrices with examples.

Let’s begin –

What is Matrix ?

A set of mn numbers (real or imaginary) arranged in the form of a rectangular array of m rows and n columns is called an m × n matrix (to be read as m by n matrix).

A m by n matrix is usually written as

A = [a11a12a1na21a22a2n...am1am2amn]

Different Types of Matrices

All different types of matrices with examples are given below :

Row Matrix

A matrix having only one row is called a row matrix or a row-vector.

Example : A = [ 1 2 -1 2 ] is a row matrix of order 1×4.

Column Matrix

A matrix having only one column is called a column matrix or a column vector.

Example : [121] is a column matrix of order 3×1.

Square Matrix

A matrix in which number of rows is equal to the number of columns, say n, is called a square matrix of order n.

Example : the matrix [211325153] is a square matrix of order 3×3 in which diagonal elements are 2, -2 and -3.

Diagonal Matrix

A square matrix A = [aij]n×n is called a diagonal matrix if all the elements, except those in the leading diagonal are zero.

Example : the matrix [100020003] is a diagonal denoted by A = diag [1, 2, 3].

Scalar Matrix

A square matrix A = [aij]n×n is called a scalar matrix if

(i) aij = 0 for all i j and,

(ii) aii = c, for all i, where c 0

In other words, a diagonal matrix in which all the diagonal elements are equal is called the scalar matrix.

Example : the matrix [2002] is scalar martix of order 2.

Identity or Unit Matrix

A square matrix A = [aij]n×n is called a identity or unit matrix if

(i) aij = 0 for all i j and,

(ii) aii = 1, for all i

In other words, a diagonal matrix in which all the diagonal elements is unity is called the unit matrix.

The identity matrix of order n is denoted by In.

Example : the matrix I2 = [1001] is identity matrix of order 2.

Null Matrix

A matrix in which al elements are zero is called  a null or a zero matrix,

Example : the matrix [0000] is null matrix of order 2.

Upper Triangular Matrix

A square matrix A = [aij] is called an upper triangular matrix if aij = 0 for all  i > j.

Thus, in an upper triangular matrix, all elements below the main diagonal are zero.

Example : [134045007] is a upper triangular matrix.

Lower Triangular Matrix

A square matrix A = [aij] is called an lower triangular matrix if aij = 0 for all  i < j.

Thus, in an lower triangular matrix, all elements above the main diagonal are zero.

Example : [100230165] is a lower triangular matrix.

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