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Student Support Forum: 'Solving a symbolic matrix/eigenvector equation.' topicStudent Support Forum > General > "Solving a symbolic matrix/eigenvector equation."

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10/31/03 08:37am

I want to symbolically solve a matrix equation, and I am not getting anywhere. My problem is that I want to test if a set of vectors p_{1...3} are eigenvectors of a (complex) matrix M. I construct this matrix M from two matrices T (Hermiian, PSD) and Q (complex, but not Hermitian or PSD). Matrix M is defined as a function of T and Q as follows:
   M = (Inverse[T]*Q)*     (Inverse[T]*Conjugate[Transpose[Q]])

   Assume further that the eigenvalues are r_{1...3} (for p_{1...3}), so that both the eigenvalues and the elements of the p vectors are elements of T and Q.

   I could test the eigenvectors of M either by calculating Eigenvectors[M] and checking what the result is, or by simply solving
and visually checking that this is equal to r_i*p_i.

   I have tried doing this by hand, but it gets rather messy (every time a different answer!), so I have now tried with Mathematica. The problem is that the system has crashed on me (excessive use of memory of MathKernel), so I am obviously doing something wrong.

   Many thanks for your help.

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