generalized eignvalues/eignvectors
显示 更早的评论
I want to solve the following generalized eignvalues/eignvector problem:
A*w=D*B*w
Where A is my first square matrix and B my second one, D is the eignvalues and w contains the eignvectors.
I tried to look at https://www.mathworks.com/help/matlab/ref/eig.html#d120e309738 but I did not get the same form I want.
is it just enough to state my problem as the following:
[w,D]=eig(A,B)
or there is another solution. Any suggestion? Thanks very much
3 个评论
Bruno Luong
2020-9-4
编辑：Bruno Luong
2020-9-4
I think your formulation is wrong (or more milly said not "standard"). The eigen value generalized decomposition is
% right eigen vectors
A*V = B*V*D
% left eigen vectors
W'*A = D*W'*B
Where D is diagonal.
Only with these forms that you can arrange with diagonal element of D (eigen values) and colums of V or W (right/left eigen vectors) to satisfy eigen equations.
In the strange form you wrote there is no separation equation between eigen vectors.
David Goodmanson
2020-9-5
Hello MA,
For the w matrix, one finds column eigenvectors, each with its own eigenvalue, and concatenates them to produce w. Is it the case that for each eigenevector u and its associated eigenvalue lambda, you are solving the equation
A*u = lamda*B*u?
Because if so, the correct resulting equation is
A*w = B*w*D
where D is the diagonal matrix of eigenvalues, and it multiplies on the right. You obtain the generalized eigenvalue form that is solved by Matlab.
Bruno Luong
2020-9-5
编辑：Bruno Luong
2020-9-5
The left eigen vectors
w'A= lamdda*w'*B % marix equation: W'*A = D*W'*B
can also be returned by MATLAB with 3-output syntax of EIG
[~,D,W] = eig(A,B)
w is columns of W, lambda diagonal elements of D.
Note that both left/right can be also obtained by Schur's decomposition with MATLAB QZ, but this is another topic.
回答（1 个）
Asad (Mehrzad) Khoddam
2020-9-4
If you multiply both sides by inv(D) we will have:
B*w = inv(D) * A * B
So you can use:
[w, invD] = eig(B, A);
D = inv(InvD);
3 个评论
David Goodmanson
2020-9-5
Hi Asad,
you meant to say
B*w = inv(D) * A * w
but unfortunately that is not in the specified form for either the left or right generalized eigenvalue problem.
Asad (Mehrzad) Khoddam
2020-9-5
Yes, you are right
MA
2020-9-5
类别
在 帮助中心 和 File Exchange 中查找有关 Linear Algebra 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
