Get the eigenvalue of a known eigenvector

I have a matrix M1 of 784x784, where each column is an eigenvector. I am looking for a way to get the eigenvalues for each eigenvector and store them in another matrix M2 of 784x1.

The matrix M3 is a matrix of 784x300. M1 contains eigenvectors of M3.

[Matt J]

The matrix M3 is a matrix of 784x300. M1 contains eigenvectors of M3.

Non-square matrices cannot have eigenvectors.

Answer 1

[John D'Errico]

What basic property do you know about the eigenvalues and eigenvectors? Come on, if you are using them, you ought to know!

If v is en eigenvector of the matrix A, then what do you know about A*v? How does that product relate to the original vector v?

If each column of the matrix V is an eigenvector, then what does A*V give you? Can you determine the eigenvalues from that product?

[Sam R]

Well, I'm trying to do basically this in Matlab, but I keep getting another matrix instead of a scalar as a result of the division.

So basically

v1 = [1; 0; 1];
v2 = A*v1;

Which would make

v2 = [2; 0; 2];

Then I thought I'd get the eigenvalue by doing

l = v2./v1;

But it gives me a column vector, and I need a scalar.

Not really sure how to do this in Matlab.

[Torsten]

Search for a nonzero component i in v1 and calculate l as

l = v2(i)/v1(i)

Best wishes

Torsten.