General Contents

Matrix Multiplication, Cayley-Hamilon Theorem, Characteristic Equation, Determinant, Eigenvalues, Derivatives, Integrals,

Matrices

Matrix Multiplication

One-By-Three_Three-By-Two one by three matrix

one by three matrix

*

three by two matrix

Three-By-Three_Three-By-Three three by three matrix

three by three matrix

*

three by three matrix

Two-By-Three_Three-By-One

┌				┐		┌		┐
│	2	1	4	│	*	│	-2	│
│	-1	0	5	│		│	6	│
└				┘		│	3	│
						└		┘

Two-By-Three_Three-By-Three

┌				┐		┌				┐
│	4	1	5	│		│	1	-4	5	│
│	3	-2	1	│	*	│	3	2	0	│
└				┘		│	-2	-3	2	│
						└				┘

Two-By-Three_Three-By-Two

┌				┐		┌			┐
│	4	1	5	│		│	1	-4	│
│	3	-2	1	│	*	│	3	2	│
└				┘		│	-2	-3	│
						└			┘

Example 1: Find matrix product to be distributed

matrix product to be distributed

where

3x3 matrix

,

3x3 matrix

, and

3x1 matrix

Determinants, Characteristic Equation, and Eigenvalues

Eigenvalue problem involving characteristic equation and determinants: 2x2 matrix of constants

Eigenvalue problem involving characteristic equation and determinants: 2x2 matrix of variables

Eigenvalue problem involving characteristic equation and determinants: 3x3 matrix of constants

Cayley-Hamilton Theorem

Cayley-Hamilton and

Cayley-Hamilton problem: 2x2 matrix of constants

Cayley-Hamilton and

Cayley-Hamilton problem: 2x2 matrix of variables

Cayley-Hamilton and

Cayley-Hamilton problem: 3x3 matrix of constants

Derivative of a Matrix

Derivative of a matrix of powers:

Matrix of powers to be differentiated

Derivative of a matrix of transcendentals:

Matrix of transcendentals to be differentiated

Integral of a Matrix

Integral of a matrix of powers:

Matrix of powers to be integrated

Integral of a matrix of transcendentals:

Matrix of transcendentals to be integrated

General Contents