The rank and eigenvalues of main diagonal perturbed matrices. (English) Zbl 0682.15007

Furth, Dave; Sierksma, Gerard

Linear Multilinear Algebra 25, No. 3, 191-204 (1989).

An \(n\times n\) matrix T is in the class \(M_ k\) if T can be written as the sum of a diagonal matrix and a matrix of rank k. Matrices of the class \(M_ 1\), on which this paper concentrates in respect of the location of their eigenvalues, occur in the economic theory of (homogeneous) oligopoly. A general result states that \(M_{n-1}=M_ n\), but for \(k=0,...,n-2\), \(M_ k\) is contained strictly in \(M_{k+1}\).

Reviewer: Eugene Seneta (Sydney)

MSC:

15A18	Eigenvalues, singular values, and eigenvectors
15A03	Vector spaces, linear dependence, rank, lineability
91B28	Finance etc. (MSC2000)
91A40	Other game-theoretic models

Keywords:

rank; eigenvalues; main diagonal perturbed matrices; input-output Leontief model; oligopoly-like games

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