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

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Atik Faysal
Atik Faysal 2020-9-23
回答： Steven Lord 2020-9-23
[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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Bruno Luong
Bruno Luong 2020-9-23
编辑：Bruno Luong 2020-9-23
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.

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Steven Lord
Steven Lord 2020-9-23
You might find the "Eigenvalues and Singular Values" chapter in Cleve Moler's Numerical Computing with MATLAB, available here, useful.

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