However, I have found a quite simple ad hoc fix, that seem to work quite Problem, the eigenvalue problem for a unitary matrix should in general be Mathematica fails on extracting the correct eigenvectors. Several uses, and it is a bit of a catastrophe (at least for me) if The eigenvalues of a unitary matrix isĪlways ☑ or complex conjugate pairs of modulus one. Unitary matrices are sometimes alsoĬalled orthogonal matrices, and have the property that their inverse isĮqual to the transpose of the matrix. This failure for unitary matrices might be special for Mathematica 4.0.0.0 If I try with 4x4, 6圆 orĨx8 unitary matrices, the Mathematica kernel crashes after a few trials.
Rate for 5x5 unitary matrices is 44%, for 7x7 unitary matrices 60% and forĩx9 unitary matrices 73% for one thousand trials. Real 3x3 matrices give zero failures for ten thousand trials. Randomised real Hermitian 3x3 matrices or randomised arbitrary I have written a short program, which tests the Eigensystem on randomlyĬhosen real unitary 3x3 matrices, and then find a failure in approx 18 % of Some further comments on Eigensystem applied to unitary matrices: Subject: Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.Re: Eigensystem applied to a unitary matrix crashes Mathematica 4. Services & Resources Wolfram Forums MathGroup Archive Finance, Statistics & Business Analysis.Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Data Framework Semantic framework for real-world data.
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