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matlabmatrixlinear-algebraeigenvalue

How can I find the joint eigenvalues of two matrices in MATLAB?

If the joint eigenvalues of matrices A and B are defined as the roots of the equation det(lambda * A - B) = 0, how can I solve this in MATLAB?

In particular, I am not sure how exactly lambda is defined - it obviously needs to be a matrix or vector, as otherwise there would only be one joint eigenvalue. Also, I am not sure if there is any in-built function, or if, say, fzero for finding the roots of nonlinear functions needs to be used.

Solution

  • There is a built-in function for this.

    http://www.mathworks.com/help/matlab/ref/eig.html

    [V,D] = eig(B,A);

    [V,D] = eig(A,B) solves the system det(A - lambda*B) == 0. However, the desired system to solve is det(A*lambda - B) == 0 and so the inputs are reversed to respect solving this system.