A Hermitian Toeplitz matrix is unitarily similar to a real Toeplitz-plus-Hankel matrix

1991 ◽  
Vol 39 (9) ◽  
pp. 2146-2148 ◽  
Author(s):  
D.M. Wilkes ◽  
S.D. Morgera ◽  
F. Noor ◽  
M.H. Hayes
Keyword(s):  
Toeplitz Matrix ◽  
Hankel Matrix

The Explicit Inverses of CUPL-Toeplitz and CUPL-Hankel Matrices

2017 ◽  
Vol 7 (1) ◽  
pp. 38-54 ◽  
Author(s):  
Zhao-Lin Jiang ◽  
Xiao-Ting Chen ◽  
Jian-Min Wang
Keyword(s):  
Toeplitz Matrix ◽  
Hankel Matrix ◽  
Structured Matrices ◽  
Hankel Matrices ◽  
The Stability

AbstractIn this paper, we consider two innovative structured matrices, CUPL-Toeplitz matrix and CUPL-Hankel matrix. The inverses of CUPL-Toeplitz and CUPL-Hankel matrices can be expressed by the Gohberg-Heinig type formulas, and the stability of the inverse matrices is verified in terms of 1-, ∞- and 2-norms, respectively. In addition, two algorithms for the inverses of CUPL-Toeplitz and CUPL-Hankel matrices are given and examples are provided to verify the feasibility of these algorithms.

scholarly journals Toeplitz nonnegative realization of spectra via companion matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 230-245
Author(s):  
Macarena Collao ◽  
Mario Salas ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Half Plane ◽  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Nonnegative Matrix ◽  
Inverse Eigenvalue Problem ◽  
Complex Numbers ◽  
Inverse Eigenvalue ◽  
Companion Matrices ◽  
Solution Matrix

Abstract The nonnegative inverse eigenvalue problem (NIEP) is the problem of finding conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum Λ = {λ1, . . ., λn}. If the problem has a solution, we say that Λ is realizable and that A is a realizing matrix. In this paper we consider the NIEP for a Toeplitz realizing matrix A, and as far as we know, this is the first work which addresses the Toeplitz nonnegative realization of spectra. We show that nonnegative companion matrices are similar to nonnegative Toeplitz ones. We note that, as a consequence, a realizable list Λ= {λ1, . . ., λn} of complex numbers in the left-half plane, that is, with Re λi≤ 0, i = 2, . . ., n, is in particular realizable by a Toeplitz matrix. Moreover, we show how to construct symmetric nonnegative block Toeplitz matrices with prescribed spectrum and we explore the universal realizability of lists, which are realizable by this kind of matrices. We also propose a Matlab Toeplitz routine to compute a Toeplitz solution matrix.

A Real-Valued Toeplitz Matrix Method for DOA Estimation

2020 ◽  
Vol 43 (4) ◽  
pp. 350-356
Author(s):  
Jianxiong Li ◽  
Deming Li ◽  
Xianguo Li
Keyword(s):  
Toeplitz Matrix ◽  
Matrix Method ◽  
Doa Estimation
Sign in / Sign up

Export Citation Format

Share Document