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

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[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.
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KSSV el 23 de Sept. de 2020
Eigen values are very basic..they are the solution/ roots of det(A-lambda*B)=0.

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Bruno Luong
Bruno Luong el 23 de Sept. de 2020
Editada: Bruno Luong el 23 de Sept. de 2020
for each column number j,
A*V = B*V*D
A*xj = lambdaj*B*xj
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.

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Steven Lord
Steven Lord el 23 de Sept. de 2020
You might find the "Eigenvalues and Singular Values" chapter in Cleve Moler's Numerical Computing with MATLAB, available here, useful.


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