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The rank and eigenvalues of main diagonal perturbed matrices. (English) Zbl 0682.15007
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 \(M_{k+1}\).

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