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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

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□□

log_□

θ

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∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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eigenvalues (

3	2	4
2	0	2
4	2	3

)

Solution

λ=−1 with multiplicity of 2, λ=8

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(

3	2	4
2	0	2
4	2	3

)

Matrix eigenvalues

Let A be a square matrix, η a vector and λ a scalar that satisfy Aη=λη,
then λ is called the eigenvalue associated with the eigenvector η of A

The eigenvalues of A are the roots of the characteristic equation det(A−λ I)=0

det((

3	2	4
2	0	2
4	2	3

)−λ(

1	0	0
0	1	0
0	0	1

)): −λ³+6λ²+15λ+8

Solve −λ³+6λ²+15λ+8=0: λ=−1 with multiplicity of 2, λ=8

The eigenvalues are:

λ=−1 with multiplicity of 2, λ=8

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Hi, ask a question about eigenvalues (

3	2	4
2	0	2
4	2	3

)

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Notebook

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

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