engleski

On a decomposition of partitioned $J$-unitary matrices

We propose a new decomposition of hyperbolic block-unitary matrices into a product of a hyperbolic block-rotation and a block-diagonal hyperbolic unitary matrix. A similar result is known in the real space equipped with the Euclidean scalar product, but we generalize it to the complex spaces equipped with hyperbolic scalar products. We shall also present an example how such a decomposition might be used to calculate other decompositions with block-operations.

hyperbolic scalar product; decomposition; 2HSVD; semidefinite $J$-polar decomposition; unitary matrices; matrix root; indefinite QR; hyperbolic CS decomposition

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