Diagonalization and spectral decomposition of factor block circulant matrices
نویسندگان
چکیده
منابع مشابه
An application of the modified Leverrier-Faddeev algorithm to the singular value decomposition of block-circulant matrices and the spectral decomposition of symmetric block- circulant matrices
The Leverrier-Faddeev algorithm, as modified by Gower (1980), is little-known but is useful for deriving the algebraic, rather than numerical, spectral structure of matrices occurring in statistical methodology. An example is given of deriving explicit forms for the singular value decomposition of any block-circulant matrix and the spectral decomposition of any symmetric block-circulant matrix....
متن کاملEigenvectors of block circulant and alternating circulant matrices
The eigenvectors and eigenvalues of block circulant matrices had been found for real symmetric matrices with symmetric submatrices, and for block circulant matrices with circulant submatrices. The eigenvectors are now found for general block circulant matrices, including the Jordan Canonical Form for defective eigenvectors. That analysis is applied to Stephen J. Watson’s alternating circulant m...
متن کاملBlock Diagonalization of Nearly Diagonal Matrices
In this paper we study the effect of block diagonalization of a nearly diagonal matrix by iterating the related Riccati equations. We show that the iteration is fast, if a matrix is diagonally dominant or scaled diagonally dominant and the block partition follows an appropriately defined spectral gap. We also show that both kinds of diagonal dominance are not destroyed after the block diagonali...
متن کاملFast block diagonalization of k-tridiagonal matrices
In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e.g., another derivation of a very recent result on generalized k-Fibonacci numbers in [M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456– 4461]; efficient (symbolic) algorithm for...
متن کاملThe Limiting Spectral Measure for the Ensemble of Generalized Real Symmetric Block m-Circulant Matrices
Given an ensemble of N × N random matrices with independent entries chosen from a nice probability distribution, a natural question is whether the empirical spectral measures of typical matrices converge to some limiting measure as N → ∞. It has been shown that the limiting spectral distribution for the ensemble of real symmetric matrices is a semi-circle, and that the distribution for real sym...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1988
ISSN: 0024-3795
DOI: 10.1016/0024-3795(88)90124-3