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Mathematics
Linear and Abstract Algebra
Types of complex matrices, why only 3?
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[QUOTE="SeM, post: 5892040"] Hi, the three main types of complex matrices are: 1. Hermitian, with only real eigenvalues 2. Skew-Hermitian , with only imaginary eigenvalues 3. Unitary, with only complex conjugates. Shouldn't there be a fourth type: 4. Non-unitary-non-hermitian, with one imaginary value (i.e. 3i) and a complex conjugate (i.e. 4+5i) ? Can such a forth type be transformed in some fashion? It is not diagonalizable, not normal and not-Hermitian. I have looked into the [URL='https://en.wikipedia.org/wiki/Foldy%E2%80%93Wouthuysen_transformation']Foldy–Wouthuysen transformation [/URL], but am not sure this will work on a complex matrix. Are there any possibilities to transform a matrix of class 4 to one of class 1, such as using Gauss Elimination? Thanks! [/QUOTE]
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Forums
Mathematics
Linear and Abstract Algebra
Types of complex matrices, why only 3?
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