On the factorization of hyperbolic and unitary transformations into rotations
(2006) SIAM Journal on Matrix Analysis and Applications — Vol. 27, n° 3, p. 876-890 (2006)
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- Abstract
- This paper presents a Σ-unitary analogue to the CS decomposition of a partitioned unitary matrix. The hyperbolic rotations revealed by the decomposition are shown to be optimal in that, among a broader class of decompositions of Σ-unitary matrices into elementary hyperbolic rotations, they are the smallest possible in a sum-of-squares sense. A similar optimality property is shown to hold for the sines in the CS decomposition of a unitary matrix.
- Affiliations
GSU Department of Mathematics
Citations
Stewart, M., & Van Dooren, P. (2006). On the factorization of hyperbolic and unitary transformations into rotations. SIAM Journal on Matrix Analysis and Applications, 27(3), 876-890. https://doi.org/10.1137/050635328 (Original work published 2006)