Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product

Pubblicato

2006-01-01

Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product

Parole chiave:

Pseudo-unitary, Pseudo-euclidean, Self-adjoint, Orthogonal, 2000 Mathematics Subject Classification, Primary: 15A21, Secondary: 15A57 (en)

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PDF (English)

Autori

Long Island University, USA
Long Island University, USA

Abstract (en)

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

Riferimenti bibliografici

J. Bognar, Indefinite Inner Products, Springer-Verlag, New York-Heidelberg, 1974.

D. Z. Djokovic, J. Patera, P. Winternitz '& ; H. Zassenhaus, Normal forms of elements of classical real and complex Lie and Jordan algebras, J. Math. Phys. 4 (6) (1983), 1363-1374.

W. Greub, Linear Algebra, Fourth Ed., Springer-Verlag, New York, 1984.

L. Kronecker, Algebraische Reduction der Schaaren bilinearer Formen, Sitzungsber. Akad. Wiss Berlin (1890), 763-767.

A. I. Mal‘Cev, Foundations of Linear Algebra, W.H. Freeman and Company, San Francisco and London, 1963.

V. Mehrmann & H. Xu, Structured Jordan canonical forms for structured matrices that are hermitian, skew hermitian or unitary with respect to indefinite inner products, The Electronic Journal of Linear Algebra, 5 (1999), 67-103.

G. E. Shilov, Linear Algebra, Dover Publications, New York, 1977.

F. Uhlig, A Canonical Form for a Pair of Real Symmetric Matrices That Generate a Nonsingular Pencil, Linear Algebra and its Applications 14 (1976), 189-209.

K. Weierstrass, Zur Theorie der bilinearen und quadratischen Formen, Monatsber. Akad. Wiss. Berlin (1868), 310-338.

Come citare

APA

Shahla e Sheldon. (2006). Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product. Revista Colombiana de Matemáticas, 40(1), 15–29. https://revistas.unal.edu.co/index.php/recolma/article/view/94635

ACM

[1]

Shahla e Sheldon 2006. Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product. Revista Colombiana de Matemáticas. 40, 1 (gen. 2006), 15–29.

ACS

(1)

Shahla; Sheldon. Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product. rev.colomb.mat 2006, 40, 15-29.

ABNT

SHAHLA; SHELDON. Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product. Revista Colombiana de Matemáticas, [S. l.], v. 40, n. 1, p. 15–29, 2006. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94635. Acesso em: 22 gen. 2025.

Chicago

Shahla, e Sheldon. 2006. «Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product». Revista Colombiana De Matemáticas 40 (1):15-29. https://revistas.unal.edu.co/index.php/recolma/article/view/94635.

Harvard

Shahla e Sheldon (2006) «Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product», Revista Colombiana de Matemáticas, 40(1), pagg. 15–29. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/94635 (Consultato: 22 gennaio 2025).

IEEE

[1]

Shahla e Sheldon, «Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product», rev.colomb.mat, vol. 40, n. 1, pagg. 15–29, gen. 2006.

MLA

Shahla, e Sheldon. «Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product». Revista Colombiana de Matemáticas, vol. 40, n. 1, gennaio 2006, pagg. 15-29, https://revistas.unal.edu.co/index.php/recolma/article/view/94635.

Turabian

Shahla, e Sheldon. «Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product». Revista Colombiana de Matemáticas 40, no. 1 (gennaio 1, 2006): 15–29. Consultato gennaio 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94635.

Vancouver

1.

Shahla, Sheldon. Reduction to normal form of a self-adjoint linear transformation with respect to a pseudo-unitary or a pseudo-euclidean inner product. rev.colomb.mat [Internet]. 1 gennaio 2006 [citato 22 gennaio 2025];40(1):15-29. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/94635