Eigenvectors of a 3D eigenvalue matrices

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?

[Matt J]

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

[Pseudoscientist]

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

Answer 1

[Jaswanth]

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.

[Christine Tobler]

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).