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1
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Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

100%
Abdikalykov A. K., Chugunov V. N., Ikramov K. D.
Special Matrices
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2015
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tom 3
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nr 1
EN
Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.
2
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A variant of the reciprocal super Catalan matrix

81%
Kılıç E., Akkus I., Kızılaslan G.
Special Matrices
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2015
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tom 3
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nr 1
EN
Recently Prodinger [8] considered the reciprocal super Catalan matrix and gave explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues were also presented. In this paper, we define and study a variant of the reciprocal super Catalan matrix with two additional parameters. Explicit formulæ for its LU-decomposition, LUdecomposition of its inverse and the Cholesky decomposition are obtained. For all results, q-analogues are also presented.
3
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The reciprocal super Catalan matrix

81%
Prodinger H.
Special Matrices
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2015
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tom 3
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nr 1
EN
The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.
4
Content available remote

Determinants and inverses of circulant matrices with complex Fibonacci numbers

61%
Altınışık E., Feyza Yalçın N., Büyükköse Ş.
Special Matrices
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2015
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tom 3
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nr 1
EN
Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.
5
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Patterns with several multiple eigenvalues

52%
Dorsey J., Johnson C. R., Wei Z.
Special Matrices
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2014
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tom 2
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nr 1
EN
Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.
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