REDUCTION TO NORMAL FORM OF A SELF-ADJOINT LINEAR TRANSFORMATION WITH RESPECT TO A PSEUDO-UNITARY OR A PSEUDO-EUCLIDEAN INNER PRODUCT

Ahdout, Shahla; Rothman, Sheldon

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.40 no.1 Bogotá Jan./June 2006

REDUCTION TO NORMAL FORM OF A SELF-ADJOINT LINEAR TRANSFORMATION WITH RESPECT TO A PSEUDO-UNITARY OR A PSEUDO-EUCLIDEAN INNER PRODUCT

Shahla Ahdout

e-mail: sahdout@liu.edu

Sheldon Rothman

e-mail: srothman@liu.edu

Mathematics Department Long Island University NY 11548 Brookville, USA

ABSTRACT. We provide a self-contained and constructive approach to reduce a self-adjoint linear transformation defined on a pseudo-unitary (resp., pseudo- euclidean) space to a canonical form.

Keywords and phrases. Pseudo-unitary, pseudo-euclidean, self-adjoint, orthogonal.

2000 Mathematics Subject Classification. Primary: 15A21. Secondary: 15A57.

RESUMEN. Nosotros damos una aproximación auto-contenida y constructiva para reducir una transformación lineal auto-adjunta definida sobre un espacio pseudo-unitario (resp. pseudo-euclidiano) a una forma canónica.

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(Recibido en septiembre de 2005. Aceptado en marzo de 2006)