Block Toeplitz Matrices: Multiplicative Properties
نویسندگان
چکیده
Given A, B, C, and D, block Toeplitz matrices, we will prove the necessary sufficient condition for AB - CD = 0, to be a matrix. In addition, with respect change of basis, characterization normal matrices entries from algebra diagonal is also obtained.
منابع مشابه
Rank properties of a sequence of block bidiagonal Toeplitz matrices
In the present paper, we proposed a new efficient rank updating methodology for evaluating the rank (or equivalently the nullity) of a sequence of block diagonal Toeplitz matrices. The results are applied to a variation of the partial realization problem. Characteristically, this sequence of block matrices is a basis for the computation of the Weierstrass canonical form of a matrix pencil that ...
متن کاملHigh Performance Algorithms for Toeplitz and block Toeplitz matrices
High Performance Algorithms for Toeplitz and block Toeplitz matrices
متن کاملLU -factorization of Block Toeplitz Matrices
We give a review of the theory of factorization of block Toeplitz matrices of the type T = (Ti−j)i,j∈Zd , where Ti−j are complex k × k matrices, in the form T = LDU, with L and L−1 lower block triangular, U and U−1 upper block triangular Toeplitz matrices, and D a diagonal matrix function. In particular, it is discussed how decay properties of Ti a ect decay properties of L, L−1, U , and U−1. W...
متن کاملToeplitz Block Matrices in Compressed Sensing
Recent work in compressed sensing theory shows that n×N independent and identically distributed (IID) sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if n N . Motivated by signal processing applications, random filtering with Toeplitz sensing matrices whose elements are drawn fro...
متن کاملMultigrid Methods for Block Toeplitz Matrices
We extend the theory of Multigrid methods developed for PDE, Toeplitz and related matrices to the Block Toeplitz case. Prolongations and restrictions are defined depending on the zeroes of the generating function of the Block Toeplitz matrix. On numerical examples we compare different choices for prolongations and restrictions.
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: Matematika (Kuala Lumpur)
سال: 2023
ISSN: ['0127-8274', '0127-9602']
DOI: https://doi.org/10.11113/matematika.v39.n1.1437