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arXiv · 1605.07103

Decomposing Real Square Matrices via Unitary Diagonalization

Théo Trouillon·Christopher R. Dance·Éric Gaussier·Guillaume Bouchard
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Abstract

Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a matrix and its transpose, which relates to unitary diagonalization. As stated by the spectral theorem, only normal matrices are unitarily diagonalizable. However we show that all real square matrices are the real part of some unitarily diagonalizable matrix.

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Théo Trouillon, Christopher R. Dance, Éric Gaussier, Guillaume Bouchard. 2016-05-23. Decomposing Real Square Matrices via Unitary Diagonalization. https://arxiv.org/abs/1605.07103

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