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Eigenvalues and eigenvectors 
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#1
May513, 01:18 AM

P: 102

can someone PLEASE explain eigenvalues and eigenvectors and how to calculate them or a link to a site that teaches it simply?



#2
May513, 01:18 AM

P: 102

Ive already read the wiki and asked my math teacher, he doesnt even know what they are.



#3
May513, 01:22 AM

P: 24

I think that Khan Academy does a great job explaining just that!
http://www.khanacademy.org/math/line...deigenvectors Also, don't forget that there's a "Math & Science Learning Materials" forum on this website; it might be a better place to check in the future. 


#4
May513, 08:04 AM

Math
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PF Gold
P: 39,361

Eigenvalues and eigenvectors
Do you know what "vectors" and "linear transformations" are? Do you know what a "linear vector space" is?



#5
May513, 10:16 AM

P: 356

A linear operator is a function that maps one vector space into another, there are certain vectors which when transformed by the linear operator, comes out as a scalar multiple of itself, the vector is the eigenvector and the multiple is the eigenvalue. 


#6
May513, 10:47 PM

P: 102

dont judge me but how does one map one vector space onto another?



#7
May513, 10:59 PM

P: 102

he doesnt know what a vector space even is! And the wiki doesnt do much to even seperate it from vectors.



#8
May513, 11:23 PM

C. Spirit
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P: 5,447

Let ##V## be a vector space over ##F## and let ##T:V\rightarrow V## be a linear operator. We say ##v\in V\setminus \left \{ 0 \right \}## is an eigenvector of ##T## if there exists a ##\lambda\in F## such that ##T(v) = \lambda v##. We call ##\lambda## an eigenvalue of ##T##.
As an example, let ##V = M_{n\times n}(\mathbb{R})## and let ##T:V\rightarrow V,A \mapsto A^{T}##. We want to find the eigenvalues of ##T##. Let ##A\in V## such that ##T(A) = A^{T} = \lambda A##. Note that ##T(T(A)) = \lambda ^{2}A = (A^T)^T = A## hence ##A(\lambda^{2}  1) = 0## and since eigenvectors have to be nonzero, this implies ##\lambda = \pm 1##. 


#9
May613, 08:37 AM

P: 102

thanks!



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