Topic
Spectrum of a matrix
About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.
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TL;DR: The spectral radius of a complex square matrix A is given by ρ ( A ) = lim sup k → ∞ (Tr A k ) 1/k as discussed by the authors, which gives information about the moduli of all eigenvalues of A.
1 citations
01 Dec 1961
1 citations
TL;DR: For a bicontractive operator T on a Kreĭ space, the connections between its eigen values and eigenstructure and the eigenvalues and eigstructure of its minimal unitary dilation U are studied in this paper.
Abstract: For a bicontractive operator T on a Kreĭ space the connections between its eigenvalues and eigenstructure and the eigenvalues and eigenstructure of its minimal unitary dilation U are studied. For eigenvalues on the unit circle of T in general only part of the eigenspace of T will return its an eigenspace of U and the corresponding eigenvalue will be a singular critical point of U.
1 citations
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TL;DR: In this paper, it was shown that the linear statistics of eigenvalues of a circulant matrix obey the Gaussian central limit theorem for a large class of input sequences.
Abstract: We show that the linear statistics of eigenvalues of circulant matrix obey the Gaussian central limit theorem for a large class of input sequences.
1 citations
TL;DR: In this paper, the interlacing properties of the eigenvalues of a symmetric matrix with those of its largest principal submatrix using root-locus ideas were derived.
Abstract: We derive the interlacing properties of the eigenvalues of a symmetric matrix with those of its largest principal submatrix using root-locus ideas. We then give a sufficient condition for distinctness of eigenvalues based on the minimality of an associated linear system.
1 citations