From symplectic eigenvalues of positive definite matrices to their pseudo-orthogonal eigenvalues | ||
| Computational Mathematics and Computer Modeling with Applications (CMCMA) | ||
| مقاله 3، دوره 1، شماره 1، شهریور 2022، صفحه 17-20 اصل مقاله (156.56 K) | ||
| نوع مقاله: Regular paper | ||
| شناسه دیجیتال (DOI): 10.52547/CMCMA.1.1.17 | ||
| نویسندگان | ||
| Kh.D. Ikramov؛ Alimohammad Nazari* | ||
| aMoscow Lomonosov State University, Moscow, Russia | ||
| چکیده | ||
| Williamson's theorem states that every real symmetric positive definite matrix $A$ of even order can be brought to diagonal form via a symplectic $T$-congruence transformation. The diagonal entries of the resulting diagonal form are called the symplectic eigenvalues of $A$. We point at an analog of this classical result related to Hermitian positive definite matrices, *-congruences, and another class of transformation matrices, namely, pseudo-unitary matrices. This leads to the concept of pseudo-unitary (or pseudo-orthogonal, in the real case) eigenvalues of positive definite matrices. | ||
| کلیدواژهها | ||
| congruence transformation؛ symplectic matrix؛ pseudo-unitary matrix؛ indices of inertia؛ Schur inequality | ||
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آمار تعداد مشاهده مقاله: 230 تعداد دریافت فایل اصل مقاله: 328 |
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