Eigenvalues and eigenvectors

1. Pseudo Epsilon

102
can someone PLEASE explain eigenvalues and eigenvectors and how to calculate them or a link to a site that teaches it simply?

2. Mathematics news on Phys.org
3. Pseudo Epsilon

102
Ive already read the wiki and asked my math teacher, he doesnt even know what they are.

Last edited by a moderator: May 5, 2013

24
5. HallsofIvy

40,229
Staff Emeritus
Do you know what "vectors" and "linear transformations" are? Do you know what a "linear vector space" is?

6. HomogenousCow

411
That is sad to hear, eigenvectors and eigenvalues are very basic maths. Teachers are very underqualified these days.

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.

7. Pseudo Epsilon

102
dont judge me but how does one map one vector space onto another?

8. Pseudo Epsilon

102
he doesnt know what a vector space even is! And the wiki doesnt do much to even seperate it from vectors.

9. WannabeNewton

5,765
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 non-zero, this implies ##\lambda = \pm 1##.

10. Pseudo Epsilon

102
thanks!

Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook
Draft saved Draft deleted