Linear maps transforming H-unitary matrices

✍ Scribed by Chi-Kwong Li; Nung-Sing Sze

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 238 KB
• Volume: 377
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2003.08.002

✦ Synopsis

Let H 1 be an n × n invertible Hermitian matrix, and let U(H 1 ) be the group of n × n H 1 -unitary matrices, i.e., matrices A satisfying A * H 1 A = H 1 . Suppose H 2 is an m × m invertible Hermitian matrix. We show that a linear transformation φ :

and φ has the form

where a, b, c and d are nonnegative integers satisfying (a

Assume H 1 has inertia (p, q) and H 2 has inertia (r, s). Then there is a linear transformation mapping U(H 1 ) into U(H 2 ) if and only if there are nonnegative integers u and v such that (r, s) = u(p, q) + v(q, p). These results generalize those of Marcus, Cheung and Li.