Eigenvalue-eigenvector structure of Schoenmakers–Coffey matrices via Toeplitz technology and applications
نویسندگان
چکیده
منابع مشابه
Hermitian Matrices, Eigenvalue Multiplicities, and Eigenvector Components
Given an n-by-n Hermitian matrix A and a real number λ, index i is said to be Parter (resp. neutral, downer) if the multiplicity of λ as an eigenvalue of A(i) is one more (resp. the same, one less) than that in A. In case the multiplicity of λ in A is at least 2 and the graph of A is a tree, there are always Parter vertices. Our purpose here is to advance the classification of vertices and, in ...
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A matrix A is said to be strictly totally positive (STP) if all its minors are strictly positive. STP matrices were independently introduced by Schoenberg in 1930 (see [13, 14]) and by Krein and Gantmacher in the 1930s. The main results concerning eigenvalues and eigenvectors of STP matrices were proved by Gantmacher and Krein in their 1937 paper [6]. (An announcement appeared in 1935 in [5]. C...
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1 Dipartimento di Matematica “Guido Castelnuovo”, SAPIENZA Università di Roma, P.le A. Moro, 2, I-00185 Roma, Italy. E-mail: [email protected]. Research supported by a grant from SAPIENZA Università di Roma. 2 Dipartimento di Matematica “Guido Castelnuovo”, SAPIENZA Università di Roma, P.le A. Moro, 2, I-00185 Roma, Italy. E-mail: [email protected]. 3 Department of Mathematic...
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The present monograph studies the asymptotic behaviour of eigenvalues, products and functions of block Toeplitz matrices generated by the Fourier coefficients of a continuous matrix-valued function. This study is based on the concept of asymptotically equivalent sequences of non-square matrices. The asymptotic results on block Toeplitz matrices obtained are applied to vector asymptotically wide...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.03.017