Displaying similar documents to “On matrices of cofactors - II”

Computing with the Square Root of NOT

De Vos, Alexis, De Beule, Jan, Storme, Leo (2009)

Serdica Journal of Computing

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To the two classical reversible 1-bit logic gates, i.e. the identity gate (a.k.a. the follower) and the NOT gate (a.k.a. the inverter), we add an extra gate, the square root of NOT. Similarly, we add to the 24 classical reversible 2-bit circuits, both the square root of NOT and the controlled square root of NOT. This leads to a new kind of calculus, situated between classical reversible computing and quantum computing.

On isometries of the symmetric space P₁(3,ℝ)

Gašper Zadnik (2014)

Colloquium Mathematicae

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We classify the isometries in the non-identity component of the whole isometry group of the symmetric space of positive 3 × 3 matrices of determinant 1: we determine the translation lengths, minimal spaces and fixed points at infinity.

Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113

N. A. Balonin, D. Ž. Ðokovic, D. A. Karbovskiy (2018)

Special Matrices

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We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders 4v with odd v ≤ 41. In this paper we cover the cases v = 43, 45, 47, 49, 51. The odd integers v < 120 for which no symmetric Hadamard matrices of order 4v are known are the following: 47, 59, 65, 67, 73, 81, 89, 93, 101, 103, 107, 109, 113, 119. By using the propus construction, we found several symmetric Hadamard matrices...

Sign patterns of J-orthogonal matrices

Frank J. Hall, Zhongshan Li, Caroline T. Parnass, Miroslav Rozložník (2017)

Special Matrices

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This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator...