A matrix is an arrangement of numbers in rows and columns and enclosed by square brackets
If a matrix has m rows and n columns then it is known as matrix of order m x n. A matrix of order m x n is written as
i) Raw Matrix:
A matrix having only one row is called a row matrix.
are the examples of row matrices.
A matrix having only one column is known as column matrix.
are the examples of Column Matrices.
A matrix is said to be square matrix which consists of equal number of rows and columns.
are the examples of Square matrices.
iv) Diagonal matrix:
A square matrix whose non-diagonal elements are zero is called a diagonal matrix.
are the examples of Diagonal Matrices.
v) Scalar Matrix:
A Diagonal Matrix whose diagonal elements are equal is called a Scalar Matrix.
are the examples of Scalar Matrix.
vi)Unit Matrix or identity Matrix:
A diagonal Matrix whose every diagonal elements are unit is called Unit Matrix. A unit matrix of (n x n) is denoted by In
are the examples of Unit Matrix.
vii)Zero Matrix(or Null Matrix):
A matrix whose every element is zero ir called a zero matrix. It is denoted by Omn
is Null Matrix.
(a) Upper Triangular Matrix:A square matrix, A = (aij), is called an upper triangular matrix if aij = 0 for i > j.
is upper triangular matrix
A square matrix is said to be upper triangular matrix if the elements below the main diagonal is zero.
b)Lower Triangular Matrix:
A square matrix A = (aij), is called lower triangular matrix if aij = 0 for i < j.
A square matrix is said to be lower triangular matrix if the elements above the main diagonal is zero.
is lower triangular matrix.
A square matrix A = (aij) is said to be symmetric matric if aij = aij for all i and j.
is symmetric matrix.
Skew Symmetric Matrix:
A square matrix A = (aij) is called skew symmetric if
aij = -aij for all i and j. Every diagonal elements of a skew symmetric matrix should be zero.
is a skew symmetric matrix.
A square matrix A is said to be Hermitian Matrix if A* = A.
Note: The diagonal elements of suh matrices should b purely real numbers.
i.e. A is Hermitian Matrix.
Skew Hermitian Matrix
A square matrix A is said to be Skew Hermitian Matrix if A* = -A i.e. if
Note: The diagonalelements of suchmatrices should be purel imaginar number or zero.
i.e. A is Skew Hermitian Matrix.
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