Eigenvectors of a 3D eigenvalue matrices

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Pseudoscientist 2022-3-18

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https://ww2.mathworks.cn/matlabcentral/answers/1674724-eigenvectors-of-a-3d-eigenvalue-matrices

评论： Christine Tobler 2023-10-11

I have three matrices called Lambda1, Lambda2 and Lambda3. The size of each matrix is 512x512x220. Lambda1 contains eigenvalues λ1 for each x, y and z, Lambda2 contains eigenvalues λ2 for each x, y and z and Lambda3 contains eigenvalues λ3 for each x, y and z.

How do I calculate eigenvectors for every x, y and z of the 512x512x220 matrix?

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Matt J 2022-3-18

You cannot calculate eigenvectors knowing only the eigenvalues and nothing else. You need the matrix that the eigenvalues came from.

Pseudoscientist 2022-3-18

Oh alright, I have that too. It is called V.

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Answer 1

Jaswanth 2023-10-11

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在 MATLAB Online 中打开

Hi Pseudoscientist,

Considering that you have the values of the mentioned three matrices, Lambda1, Lambda2, and Lambda3, each containing eigenvalues for each x, y, and z coordinate, you can create eigenvectors using the "eig" function.

Please refer the following sample code:

% Create Eigenvalues matrix
% The diag() function is used to create a diagonal matrix with these eigenvalues as its diagonal elements.
Eigenvalues = diag([lambda1, lambda2, lambda3]);
            
% Solve eigenvalue problem
[V, ~] = eig(Eigenvalues);

For more information on the functions used here, please refer to the following resources:

Hope this Helps.

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Christine Tobler 2023-10-11

As Matt J. said above, it's not possible to compute the eigenvectors given only the eigenvalues. Here you are simply constructing a new matrix, for which the eigenvectors can be computed, but they won't match the eigenvectors of the original matrix (in fact, V will just be the identity matrix here).

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