TY - JOUR
ID - 101991
TI - From symplectic eigenvalues of positive definite matrices to their pseudo-orthogonal eigenvalues
JO - Computational Mathematics and Computer Modeling with Applications (CMCMA)
JA - CMCMA
LA - en
SN -
AU - Ikramov, Kh.D.
AU - Nazari, Alimohammad
AD - aMoscow Lomonosov State University, Moscow, Russia
AD -
Y1 - 2022
PY - 2022
VL - 1
IS - 1
SP - 17
EP - 20
KW - congruence transformation
KW - symplectic matrix
KW - pseudo-unitary matrix
KW - indices of inertia
KW - Schur inequality
DO - 10.52547/CMCMA.1.1.17
N2 - 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.
UR - https://cmcma.sbu.ac.ir/article_101991.html
L1 - https://cmcma.sbu.ac.ir/article_101991_930629420cb285a6a38484522f0c0cdd.pdf
ER -