$G$-space of isotropic directions and $G$-spaces of $ \varphi $-scalars with $G=O( n,1,\mathbb {R}) $

Aleksander Misiak; Eugeniusz Stasiak

Displaying similar documents to “ $G$ -space of isotropic directions and $G$ -spaces of $ϕ$ -scalars with $G = O (n, 1, ℝ)$ ”

G-matrices, $J$ -orthogonal matrices, and their sign patterns

Frank J. Hall, Miroslav Rozložník (2016)

Czechoslovak Mathematical Journal

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A real matrix $A$ is a G-matrix if $A$ is nonsingular and there exist nonsingular diagonal matrices $D_{1}$ and $D_{2}$ such that $A^{- T} = D_{1} A D_{2}$ , where $A^{- T}$ denotes the transpose of the inverse of $A$ . Denote by $J = diag (\pm 1)$ a diagonal (signature) matrix, each of whose diagonal entries is $+ 1$ or $- 1$ . A nonsingular real matrix $Q$ is called $J$ -orthogonal if $Q^{T} J Q = J$ . Many connections are established between these matrices. In particular, a matrix $A$ is a G-matrix if and only if $A$ is diagonally (with positive diagonals) equivalent to a column permutation...

A treatment of a determinant inequality of Fiedler and Markham

Minghua Lin (2016)

Czechoslovak Mathematical Journal

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Fiedler and Markham (1994) proved ${(\frac{\det \hat{H}}{k})}^{k} \geq \det H,$ where $H = {(H_{i j})}_{i, j = 1}^{n}$ is a positive semidefinite matrix partitioned into $n \times n$ blocks with each block $k \times k$ and $\hat{H} = {(tr H_{i j})}_{i, j = 1}^{n}$ . We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove $\det (I_{n} + \hat{H}) \geq \det {(I_{n k} + k H)}^{1 / k} .$

Linear preservers of rc-majorization on matrices

Mohammad Soleymani (2024)

Czechoslovak Mathematical Journal

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Let $A$ , $B$ be $n \times m$ matrices. The concept of matrix majorization means the $j$ th column of $A$ is majorized by the $j$ th column of $B$ and this is done for all $j$ by a doubly stochastic matrix $D$ . We define rc-majorization that extended matrix majorization to columns and rows of matrices. Also, the linear preservers of rc-majorization will be characterized.

Projectively equivariant quantization and symbol on supercircle $S^{1 | 3}$

Taher Bichr (2021)

Czechoslovak Mathematical Journal

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Let $𝒟_{λ, μ}$ be the space of linear differential operators on weighted densities from $ℱ_{λ}$ to $ℱ_{μ}$ as module over the orthosymplectic Lie superalgebra $𝔬𝔰𝔭 (3 | 2)$ , where $ℱ_{λ}$ , $ł \in ℂ$ is the space of tensor densities of degree $λ$ on the supercircle $S^{1 | 3}$ . We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.

Generalized notions of amenability for a class of matrix algebras

Amir Sahami (2019)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the amenability and its related homological notions for a class of $I \times I$ -upper triangular matrix algebra, say $UP (I, A)$ , where $A$ is a Banach algebra equipped with a nonzero character. We show that $UP (I, A)$ is pseudo-contractible (amenable) if and only if $I$ is singleton and $A$ is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of $UP (I, A)$ .

Circulant matrices with orthogonal rows and off-diagonal entries of absolute value $1$

Daniel Uzcátegui Contreras, Dardo Goyeneche, Ondřej Turek, Zuzana Václavíková (2021)

Communications in Mathematics

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It is known that a real symmetric circulant matrix with diagonal entries $d \geq 0$ , off-diagonal entries $\pm 1$ and orthogonal rows exists only of order $2 d + 2$ (and trivially of order $1$ ) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries $d \geq 0$ and any complex entries of absolute value $1$ off the diagonal. As a particular case, we consider...

Analytic aspects of the circulant Hadamard conjecture

Teodor Banica, Ion Nechita, Jean-Marc Schlenker (2014)

Annales mathématiques Blaise Pascal

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We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for $| q_{0} | = ... = | q_{N - 1} | = 1$ the quantity $Φ = \sum_{i + k = j + l} \frac{q_{i} q_{k}}{q_{j} q_{l}}$ satisfies $Φ \geq N^{2}$ , with equality if and only if $q = (q_{i})$ is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of $Φ$ , (2) the study of the critical points of $Φ$ , and (3) the computation of the moments of $Φ$ . We explore here...

Linear preserver of $n \times 1$ Ferrers vectors

Leila Fazlpar, Ali Armandnejad (2023)

Czechoslovak Mathematical Journal

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Let $A = {[a_{i j}]}_{m \times n}$ be an $m \times n$ matrix of zeros and ones. The matrix $A$ is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero $(1, 1)$ -entry. We characterize all linear maps perserving the set of $n \times 1$ Ferrers vectors over the binary Boolean semiring and over the Boolean ring $ℤ_{2}$ . Also, we have achieved the number of these linear maps in each case.

Ground states of supersymmetric matrix models

Gian Michele Graf (1998-1999)

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d = 9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d = 9$ . Moreover, it would be unique. Other values of $d$ , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

Factorization of CP-rank- $3$ completely positive matrices

Jan Brandts, Michal Křížek (2016)

Czechoslovak Mathematical Journal

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A symmetric positive semi-definite matrix $A$ is called completely positive if there exists a matrix $B$ with nonnegative entries such that $A = B B^{⊤}$ . If $B$ is such a matrix with a minimal number $p$ of columns, then $p$ is called the cp-rank of $A$ . In this paper we develop a finite and exact algorithm to factorize any matrix $A$ of cp-rank $3$ . Failure of this algorithm implies that $A$ does not have cp-rank $3$ . Our motivation stems from the question if there exist three nonnegative polynomials of degree at...

Displaying similar documents to “ G -space of isotropic directions and G -spaces of ϕ -scalars with G = O ( n , 1 , ℝ ) ”

Displaying similar documents to “ $G$ -space of isotropic directions and $G$ -spaces of $ϕ$ -scalars with $G = O (n, 1, ℝ)$ ”