矩阵非齐次特征值分析

MATRIX INHOMOGENEOUS EIGENVALUE ANALYSIS

矩阵非齐次特征值分析卢旭光（清华大学应用数学系）ＭＡＴＲＩＸＩＮＨＯＭＯＧＥＮＥＯＵＳＥＩＧＥＮＶＡＬＵＥＡＮＡＬＹＳＩＳ￥ＬｕＸｕ－ｇｕａｎｇ（ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｓｔｕｄｙｔｈｅｍａｔ...

Abstract In this paper we study the matrix inhomogeneous eigenvalue problem: (A - λI)X = where A If(λ,X) ∈ C × C(n×m) is a solution to the problem, then λ is called an inhomogeneouseigenvalue of A with respect to B. Using topological and analytic methods we obtain (i)geometrical properties of the inhomogeneous eigenvalues, (ii) some sufficient conditionsfor the existence of real solutions of the problem, and (iii) some iterative methods forcomputing all complex solutions of the problem with , where K is asuitable constant, e.g. (A)