Abstract
In this paper, we propose the two-sided hyperbolic SVD (2HSVD) for square matrices, i.e., A = U Σ V [ ∗ ] , where U and V [ ∗ ] are J-unitary ( J = diag ( ± 1 ) ) and Σ is a real diagonal matrix of “double-hyperbolic” singular values. We show that, with some natural conditions, such decomposition exists without the use of hyperexchange matrices. In other words, U and V [ ∗ ] are really J-unitary with regard to J and not some matrix J ^ which is permutationally similar to matrix J. We provide full characterization of 2HSVD and completely relate it to the semidefinite J-polar decomposition.
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