Maths > Matrices and Determinants > 1.0 Introduction
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
1.3 Transpose of a 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:
The matrix obtained from any given matrix $A$ , by interchanging its rows and columns , is called the transpose of $A$ and is denoted by ${A^T}$.
Example:
If $A = \left( {\begin{array}{c} 1&2&3 \\ 4&5&6 \\ 7&8&9 \end{array}} \right)$
Then ${A^T} = \left( {\begin{array}{c} 1&4&7 \\ 2&5&8 \\ 3&6&9 \end{array}} \right)$