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Eigenvectors of a 3D eigenvalue matrices

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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?
  2 Comments
Matt J
Matt J on 18 Mar 2022
You cannot calculate eigenvectors knowing only the eigenvalues and nothing else. You need the matrix that the eigenvalues came from.
Pseudoscientist
Pseudoscientist on 18 Mar 2022
Oh alright, I have that too. It is called V.

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Answers (1)

Jaswanth
Jaswanth on 11 Oct 2023
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:
  1. “eig”: https://in.mathworks.com/help/matlab/ref/eig.html
  2. “diag”: https://in.mathworks.com/help/matlab/ref/diag.html?searchHighlight=diag&s_tid=srchtitle_support_results_1_diag
Hope this Helps.
  1 Comment
Christine Tobler
Christine Tobler on 11 Oct 2023
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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