對合酉矩陣之穩定性

Abstract

我們證明一個對合酉矩陣的 類-Krein 定理.當一對合酉矩陣之特徵值有 重根且符合該準則時,即使些微擾動它仍究保持穩定.此外,我們也探究在 固定維度中,對合酉矩陣的譜穩定區域. Let P be an involution. An analog Krein theory for P-unitary matrices was derived. It provides a criterion for P-unitary matrices to remain stable when eigenvalues collide as the matrices vary. For a fixed dimension, the spectral stability region in terms of the coefficients of the characteristic polynomials of P-unitary matrices in the space of coefficients was investigated. Some low dimensional cases are demonstrated for illustration.