✦ LIBER ✦

Absolutely indecomposable symmetric matrices

✍ Scribed by Hans A. Keller; A.Herminia Ochsenius

Book ID: 104152525
Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 127 KB
Volume: 174
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(02)00037-3

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✦ Synopsis

Let A be a symmetric matrix of size n × n with entries in some (commutative) ÿeld K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T ∈ Matn(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base ÿeld. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Matn(K) there exist symmetric, absolutely indecomposable matrices i n is congruent to 0, 1 or -1 modulo 2s.

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