Generation of Matrices with Specified Eigenvalues and their Diagonalization

Details Generation of Matrices with Specified Eigenvalues and their Diagonalization Generation of Matrices with Specified Eigenvalues and their Diagonalization

2005-06-09

arxiv.org/abs/quant-ph/0506074v1

Physics

Quantum Physics

12 pages, LateX

Scientific paper

We present a prescription for forming matrices with specified eigenvalues and known eigenvectors. With this method, we can form Hermitian, anti-Hermitian, symmetric and general matrices with arbitrary eigenvalues. In addition we propose an algorithm for diagonalizing such matrices. The functions required for the realization of this are probability amplitudes connecting observables with discrete eigenvalue spectra and can be obtained from spin theory. For the example case of $5\times 5$ matrices, these functions are given.

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