Matrix Operation

pic. 1

Let's think about possible conditions of matrix operation

by reading pic. 1.

Example

pic. 2

pic. 3

There are n x n matrices, A and B.

Every matrix has rows and columns like pic. 3.

Let's operate matrices.

pic. 4

We can operate like pic. 4.

Example

pic. 5

Examples of Matrix Operation

Cramer's Rule

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see

Properties of Determinant

I've used Gauss-Jordan Elimination 

to solve simultaneous equations.

There is another method to solve simultaneous equations,

Cramer's Rule

You can understand how to solve simultaneous equations by Cramer's rule.

Fibonacci Number

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Diagonalizable

Gauss - Jordan Elimination

Gauss - Jordan Elimination

If you solve simultaneous equations or find inverse matrix,

you can use Gauss-Jordan Elimination.

Diagonalizable

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see

Properties of Determinant

Eigenvalue in Matrix

Linear Independence and Dependence

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see

Determinant A where Ax=O

Eigenvalue in Matrix

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see

Determinant A where Ax=O

Determinant A where Ax=O

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see

Properties of Determinant

Properties of Determinant

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see

Determinant of Matrix

1. det [cA] = c^n det A

2. DETERMINANT of A MATRIX 

that is multiplied constants at a column of a certain matrix

 and added same column of another matrix 

3. determinant of exchanged 2 columns of matrix

If a_ik=a_il, where i=1,2, ... ,n, 

that means col_k [A] = col_l [A],

det A = det C.

So, det A = - det A.

Then, det A = 0.

Inverse Matrix

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Identity Matrix

Determinant of Matrix

Identity Matrix

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see

Determinant of Matrix

Determinant of Matrix

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see

Permutation, Symmetric Group and Signature

Cyclic Permutation

Matrix Operation