TY - CHAP

T1 - Canonical form for H-symplectic matrices

AU - Groenewald, G. J.

AU - Janse van Rensburg, D. B.

AU - Ran, A. C.M.

PY - 2018

Y1 - 2018

N2 - In this paper we consider pairs of matrices (A,H), with A and H either both real or both complex, H is invertible and skew-symmetric and A is H -symplectic, that is, ATH A = H. A canonical form for such pairs is derived under the transformations (A,H) → (S −1AS, STH S) for invertible matrices S. In the canonical form for the pair, the matrix A is brought in standard (real or complex) Jordan normal form, in contrast to existing canonical forms.

AB - In this paper we consider pairs of matrices (A,H), with A and H either both real or both complex, H is invertible and skew-symmetric and A is H -symplectic, that is, ATH A = H. A canonical form for such pairs is derived under the transformations (A,H) → (S −1AS, STH S) for invertible matrices S. In the canonical form for the pair, the matrix A is brought in standard (real or complex) Jordan normal form, in contrast to existing canonical forms.

KW - Canonical forms

KW - H -symplectic matrices

KW - Indefinite inner product space

UR - http://www.scopus.com/inward/record.url?scp=85060166112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060166112&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04269-1_11

DO - 10.1007/978-3-030-04269-1_11

M3 - Chapter

AN - SCOPUS:85060166112

SN - 9783030042684

T3 - Operator Theory: Advances and Applications

SP - 269

EP - 290

BT - Operator Theory, Analysis and the State Space Approach

A2 - Bart, Harm

A2 - ter Horst, Sanne

A2 - Ran, André C.M.

A2 - Woerdeman, Hugo J.

PB - Springer International Publishing Switzerland

ER -