Naslov
A Bound for the Condition of a Hyperbolic Eigenvector Matrix

Autori
Slapničar, Ivan ; Veselić, Krešimir

Izvornik
Linear Algebra and its Applications (0024-3795) 290 (1999), 1-3; 247-255

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
spectral condition; hyperbolic eigenvector matrix

Sažetak
The hyperbolic eigenvector matrix is a matrix $X$ which simultaneously diagonalizes the pair $(H, J)$, where $H$ is Hermitian positive definite and $J=diag (pm 1)$ such that $X^*HX=Delta$ and $X^*JX=J$. We prove that the spectral condition of $X$, $kappa(X)$, is bounded by $kappa(X)leq sqrt{;min kappa (D^*H D)};$, where the minimum is taken over all non-singular matrices $D$ which commute with $J$. This bound is attainable and it can be simply computed. Similar results hold for other signature matrices $J$, like in the discretized Klein-Gordon equation.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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