Inverse eigenproblem for -symmetric matrices and their approximation

✍ Scribed by Yongxin Yuan

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 464 KB
• Volume: 233
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.07.022

✦ Synopsis

Canonical correlation decomposition (CCD)

Best approximation a b s t r a c t

In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors {x i } m i=1 in C n and a set of complex numbers {λ i } m i=1 , find a matrix A ∈ GSC n×n such that {x i } m i=1 and {λ i } m i=1 are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n × n matrix Ã, find  ∈ S E such that à - = min A∈S E à -A , where S E is the solution set of IEP and • is the Frobenius norm. We provide an explicit formula for the best approximation solution  by means of the canonical correlation decomposition.