Maths > Matrices and Determinants > 3.0 Special Matrices
Matrices and Determinants
1.0 Introduction
2.0 Algebra of Matrices
3.0 Special Matrices
3.1 (a) Symmetric Matrix:
3.2 (b) Skew Symmetric Matrix:
3.3 (c) Hermitian matrix:
3.4 (d) Skew Hermitian Matrix:
3.5 (e) Singular and Non-singular Matrices:
3.6 (f) Orthogonal Matrix :
3.7 (g) Idempotent Matrix :
3.8 (h) Unitary Matrix :
3.9 (i) Involuntary Matrix:
3.10 (j) Nilpotent Matrix:
4.0 Determinant of a square matrix
5.0 Adjoint of a square Matrix
6.0 Inverse of a Matrix
7.0 Types of Equations Homogenous & Non-Homogenous
8.0 Cramer's rule
9.0 Types of Linear Equations
3.5 (e) Singular and Non-singular Matrices:
3.2 (b) Skew Symmetric Matrix:
3.3 (c) Hermitian matrix:
3.4 (d) Skew Hermitian Matrix:
3.5 (e) Singular and Non-singular Matrices:
3.6 (f) Orthogonal Matrix :
3.7 (g) Idempotent Matrix :
3.8 (h) Unitary Matrix :
3.9 (i) Involuntary Matrix:
3.10 (j) Nilpotent Matrix:
Any square matrix $A$ is said to be singular if $|A|=0$ , otherwise it is said to be non-singular
Example:
If $A$=$\left[ {\begin{array}{c} 5&{10} \\ 3&6 \end{array}} \right]$
Then |$A$| = $\left| {\begin{array}{c} 5&{10} \\ 3&6 \end{array}} \right|$=30-30=0 $ \Rightarrow $ $A$ is a singular matrix
Example:
If $A$= $\left[ {\begin{array}{c} 2&3 \\ 4&5 \end{array}} \right]$
Then |$A$| = $\left| {\begin{array}{c} 2&3 \\ 4&5 \end{array}} \right|$ = 10-12=-2 $ \Rightarrow $ $A$ is a non-singular matrix
