Displaying similar documents to “Möbius gyrovector spaces in quantum information and computation”

The Re-nonnegative definite solutions to the matrix equation A X B = C

Qing Wen Wang, Chang Lan Yang (1998)

Commentationes Mathematicae Universitatis Carolinae

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An n × n complex matrix A is called Re-nonnegative definite (Re-nnd) if the real part of x * A x is nonnegative for every complex n -vector x . In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation A X B = C are presented.

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

Jiří Rohn (2007)

Applications of Mathematics

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For a real square matrix A and an integer d ≥ 0 , let A ( d ) denote the matrix formed from A by rounding off all its coefficients to d decimal places. The main problem handled in this paper is the following: assuming that A ( d ) has some property, under what additional condition(s) can we be sure that the original matrix A possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists...

Geometric approaches to establish the fundamentals of Lorentz spaces ℝ 2 3 and ℝ 1 2

Sevilay Çoruh Şenocak, Salim Yüce (2024)

Mathematica Bohemica

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The aim of this paper is to investigate the orthogonality of vectors to each other and the Gram-Schmidt method in the Minkowski space ℝ 2 3 . Hyperbolic cosine formulas are given for all triangle types in the Minkowski plane ℝ 1 2 . Moreover, the Pedoe inequality is explained for each type of triangle with the help of hyperbolic cosine formulas. Thus, the Pedoe inequality allowed us to establish a connection between two similar triangles in the Minkowski plane. In the continuation of the study,...

A characterization of Fuchsian groups acting on complex hyperbolic spaces

Xi Fu, Liulan Li, Xiantao Wang (2012)

Czechoslovak Mathematical Journal

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Let G ⊂ 𝐒𝐔 ( 2 , 1 ) be a non-elementary complex hyperbolic Kleinian group. If G preserves a complex line, then G is ℂ -Fuchsian; if G preserves a Lagrangian plane, then G is ℝ -Fuchsian; G is Fuchsian if G is either ℂ -Fuchsian or ℝ -Fuchsian. In this paper, we prove that if the traces of all elements in G are real, then G is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an...