Can someone provide me the theory and math behind this function of eigen?

[V,D] = eig(A,B)

returns diagonal matrix D of generalized eigenvalues and full matrix V whose columns are the corresponding right eigenvectors, so that A*V = B*V*D.

[KSSV]

Eigen values are very basic..they are the solution/ roots of det(A-lambda*B)=0.

[Bjorn Gustavsson]

For a more exheustive introduction with some more details you can turn to: Eigenvalues and eigenvectors at wikipedia and Generalized eigenvectors.

Answer 1

[Bruno Luong]

for each column number j,

A*V = B*V*D

implies

A*xj = lambdaj*B*xj

where

xj = V(:,j)
lambdaj = D(j,j)

This is just a generalization of normal eigen value problem.

A*xj = lambdaj*xj

If B is invertible, V and D is the same as standard eigen vectors/values of M := inv(B)*A.

Answer 2

[Steven Lord]

You might find the "Eigenvalues and Singular Values" chapter in Cleve Moler's Numerical Computing with MATLAB, available here, useful.