can someone PLEASE explain eigenvalues and eigenvectors and how to calculate them or a link to a site that teaches it simply?
I think that Khan Academy does a great job explaining just that! http://www.khanacademy.org/math/lin...-introduction-to-eigenvalues-and-eigenvectors 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.
Do you know what "vectors" and "linear transformations" are? Do you know what a "linear vector space" is?
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.
he doesnt know what a vector space even is! And the wiki doesnt do much to even seperate it from vectors.
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##.