The properties of a kind of random symplectic matrices
Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation; 2) Its condition number is a constant; 3) The condition number of it is about 2.618.
Key wordssymplectic matrix QR-like algorithm eigenvalue condition number Jordan canonical form Schur canonical form
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