Toeplitz matrices and invertibility of Hankel matrices
نویسندگان
چکیده
منابع مشابه
Irreducible Toeplitz and Hankel matrices
An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.
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Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property–the number of times each random variable appears in the matrix is (more or less) the same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is sca...
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The paper gives a self-contained survey of fast algorithms for solving linear systems of equations with Toeplitz or Hankel coefficient matrices. It is written in the style of a textbook. Algorithms of Levinson-type and of Schur-type are discussed. Their connections with triangular factorizations, Padè recursions and Lanczos methods are demonstrated. In the case in which the matrices possess add...
متن کاملGeneralized inversion of Toeplitz-plus-Hankel matrices
In many applications, e.g. digital signal processing, discrete inverse scattering, linear prediction etc., Toeplitz-plus-Hankel (T + H) matrices need to be inverted. (For further applications see [1] and references therein). Firstly the T +H matrix inversion problem has been solved in [2] where it was reduced to the inversion problem of the block Toeplitz matrix (the so-called mosaic matrix). T...
متن کاملThe Inverses of Block Hankel and Block Toeplitz Matrices
A set of new formulae for the inverse of a block Hankel (or block Toeplitz) matrix is given. The formulae are expressed in terms of certain matrix Pad6 forms, which approximate a matrix power series associated with the block Hankel matrix. By using Frobenius-type identities between certain matrix Pad6 forms, the inversion formulae are shown to generalize the formulae of Gohberg-Heinig and, in t...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1964
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1964.14.651