Suliman Khan

To find the eigenvalues of a matrix with quaternion entries in MATLAB, you'll need to approach the problem differently since MATLAB's built-in functions for eigenvalue computation (eig) do not directly support matrices with quaternion entries. One effective approach is to convert the quaternion matrix into a larger real matrix that can be handled by standard eigenvalue algorithms. Here's how you can do it:

Steps to Convert Quaternion Matrix to Real Matrix

Detailed Steps in MATLAB

Here's a step-by-step MATLAB code to perform the conversion and compute the eigenvalues:

matlabCopy code% Define quaternion units O = quaternion(0, 0, 0, 0); % Zero L = quaternion(1, 0, 0, 0); % One i = quaternion(0, 1, 0, 0); j = quaternion(0, 0, 1, 0); k = quaternion(0, 0, 0, 1); % Define the 4x4 quaternion matrix A = [O i O L; -i O j O; O -j O -k; L O k O]; % Function to convert a quaternion to its 4x4 real matrix representation quaternion_to_real = @(q) [ real(q), -imag(q), -jmag(q), -kmag(q); imag(q), real(q), -kmag(q), jmag(q); jmag(q), kmag(q), real(q), -imag(q); kmag(q), -jmag(q), imag(q), real(q); ]; % Initialize the real matrix n = size(A, 1); real_A = zeros(4*n, 4*n); % Fill the real matrix with 4x4 blocks for r = 1:n for c = 1:n real_A(4*(r-1)+1:4*r, 4*(c-1)+1:4*c) = quaternion_to_real(A(r, c)); end end % Compute the eigenvalues of the real matrix eigenvalues = eig(real_A); % Display the eigenvalues disp('Eigenvalues:'); disp(eigenvalues);

Sandeep Jaiswal thank you for your thoughts, but unfortunately, it is still unsolved, even though I applied your method. Let me try some other techniques, hopefully, I will get something interesting.

Suliman Khan

Thanks Suliman. Sorry to hear that my solution did not workout for you. Let me know if you still have problems and I will be happy to be of any assistance.