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 = [a11a12……a1na21a22……a2n...am1am2……amn]
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 : [12−1] 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 [21−13−2515−3] 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.