@article {
author = {Ikramov, Kh.D. and Nazari, Alimohammad},
title = {From symplectic eigenvalues of positive definite matrices to their pseudo-orthogonal eigenvalues},
journal = {Computational Mathematics and Computer Modeling with Applications (CMCMA)},
volume = {1},
number = {1},
pages = {17-20},
year = {2022},
publisher = {Shahid Beheshti University},
issn = {2783-4859},
eissn = {2783-4859},
doi = {10.52547/CMCMA.1.1.17},
abstract = {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.},
keywords = {congruence transformation,symplectic matrix,pseudo-unitary matrix,indices of inertia,Schur inequality},
url = {https://cmcma.sbu.ac.ir/article_101991.html},
eprint = {https://cmcma.sbu.ac.ir/article_101991_930629420cb285a6a38484522f0c0cdd.pdf}
}