Möbius gyrovector spaces in quantum information and computation

Abraham A. Ungar

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 $n \times n$ 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 $d \geq 0$ , 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,...

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

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

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

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

Geometric approaches to establish the fundamentals of Lorentz spaces $ℝ_{2}^{3}$ and $ℝ_{1}^{2}$