Maths > Matrices and Determinants > 5.0 Adjoint of a square Matrix
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
5.1 Elementary row Transformations
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 following three types of operations on the rows of a given matrix are known as elementary row transformations:
- Interchanging any two rows of the given matrix.This transformation is indicated by ${R_{ij}}$,if the ${i^{th}}$ row and ${j^{th}}$ row are interchanged.
It is denoted by ${R_i} \leftrightarrow {R_j}$ - Multiplying every element of any row of the given matrix by a non zero number.This transformation is indicated by ${R_i}(k)$,if the multiplicaton of the ith row by a constant $k$
It is denoted by ${R_i} \to k.{R_i}$ - Addition of a constant multiple of the elements of any row to the corresponding elements of any other row.This transformation is indicated by ${R_ij}(k)$,if the addition of the ${i^{th}}$ row to the elements of the ${j^{th}}$ row multiplied by constant $k$.
It is denoted by ${R_i} \to {R_i} + k.{R_j}$
