Eigenvalues and Eigenvectors Equation Formula Latex Code and Summary

Eigenvalues and Eigenvectors

Tags: #math #eigenvalues #eigenvectors

Equation

$$A\mathbf{u}=\lambda\mathbf{u} \\ P_{n}(\lambda)=|A-\lambda I|$$

Latex Code

                                 A\mathbf{u}=\lambda\mathbf{u} \\ 
P_{n}(\lambda)=|A-\lambda I|

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Introduction

$A\mathbf{u}=\lambda\mathbf{u} \\ P_{n}(\lambda)=|A-\lambda I|$

The n eigenvalues $\lambda_{i}$ and eigenvectors $u_{i}$ of an n by n matrix A are the solutions of the equation $A\mathbf{u}=\lambda\mathbf{u}$ . The eigenvalues are the zeros of the polynomial of degree n $P_{n}(\lambda)=|A-\lambda I|$ . Additionally, $|A-\lambda I|=0$ is called the characteristic equation of the matrix.

Trace of matrix A
$\text{Tr} A=\sum_{i}\lambda_{i}$
Determinants of a matrix A
$|A|=\prod_{i} \lambda_{i}$

Discussion

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Deborah Lewis

My one wish right now is to pass this test.

2023-11-16 00:00
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Joan Campbell reply to Deborah Lewis

Gooood Luck, Man!

2023-12-07 00:00:00.0
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Paula Burton

I'm burning the midnight oil to pass this test.

2023-02-02 00:00
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Irene Cox reply to Paula Burton

Nice~

2023-02-21 00:00:00.0
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Jacob Wright

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2023-07-22 00:00
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Bonnie Simmons reply to Jacob Wright

Nice~

2023-07-22 00:00:00.0
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