Book Review: Circulant matrices
نویسندگان
چکیده
منابع مشابه
Toeplitz and Circulant Matrices: A review Toeplitz and Circulant Matrices: A review
t 0 t −1 t −2 · · · t −(n−1) t 1 t 0 t −1 t 2 t 1 t 0. .. t n−1 · · · t 0 The fundamental theorems on the asymptotic behavior of eigenval-ues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and...
متن کاملToeplitz and Circulant Matrices: A Review
t0 t−1 t−2 · · · t−(n−1) t1 t0 t−1 t2 t1 t0 .. .. . . . tn−1 · · · t0 The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hop...
متن کاملOn circulant and two-circulant weighing matrices
We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer ”YES”, by constructing a circulant weighing matrix of orde...
متن کاملApplication of Circulant Matrices
A k x k matrix A = [aU lover a field F is called circulant if aij = a (j-i) mod k' A [2k ,k l linear code over F = GF (q) is called double-circulant if it is generated by a matrix of the fonn [I A l, where A is a circulant matrix. In this work we ftrst employ the Fourier transform techJ nique to analyze and construct se:veral families of double-circulant codes. The minimum distance of the resul...
متن کاملCirculant Hadamard Matrices
Note. The determinant of a circulant matrix is an example of a group determinant, where the group is the cyclic group of order n. In 1880 Dedekind suggested generalizing the case of circulants (and more generally group de terminants for abelian groups) to arbitrary groups. It was this suggestion that led Frobenius to the creation group of representation theory. See [1] and the references therein.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1982
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1982-15054-6