Isospectral Matrix Flows Maintaining The Initial Structure
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A matrix function F(A) is said to be skew-symmetric operator if (F(A))T = -F(A). It is well known that [5] if F(A) is skew-symmetric then the solution A(t) of dA dt= [A; F(A)] A(0) = A0 maintains the spectrum of A0, where [A;B] = AB - BA: The matrix A is said to be centrosymmetric if JAJ = A, where J is the matrix with ones on the secondary diagonal and zeros elsewhere. A matrix function F(A) is said to be centrosymmetric operator if F(JAJ) = JF(A)J. In this paper we introduce a skew-symmetric and centrosymmetric operator F(A) that the solution A(t) of dAdt = [A; F(A)] A(0) = A0 maintains both, the spectrum of A0 and the initial structure of A0, that is if A0 is a staircase matrix then so is the solution A(t).
Abstract
A matrix function F(A) is said to be skew-symmetric operator if (F(A))T = -F(A). It is well known that [5] if F(A) is skew-symmetric then the solution A(t) of dA dt= [A; F(A)] A(0) = A0 maintains the spectrum of A0, where [A;B] = AB - BA: The matrix A is said to be centrosymmetric if JAJ = A, where J is the matrix with ones on the secondary diagonal and zeros elsewhere. A matrix function F(A) is said to be centrosymmetric operator if F(JAJ) = JF(A)J. In this paper we introduce a skew-symmetric and centrosymmetric operator F(A) that the solution A(t) of dAdt = [A; F(A)] A(0) = A0 maintains both, the spectrum of A0 and the initial structure of A0, that is if A0 is a staircase matrix then so is the solution A(t).
참고문헌 (8)
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