The Re-nonnegative definite solutions to the matrix equation $AXB=C$

Qing Wen Wang; Chang Lan Yang

Displaying similar documents to “The Re-nonnegative definite solutions to the matrix equation $A X B = C$ ”

On block triangular matrices with signed Drazin inverse

Changjiang Bu, Wenzhe Wang, Jiang Zhou, Lizhu Sun (2014)

Czechoslovak Mathematical Journal

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The sign pattern of a real matrix $A$ , denoted by $sgn A$ , is the $(+, -, 0)$ -matrix obtained from $A$ by replacing each entry by its sign. Let $𝒬 (A)$ denote the set of all real matrices $B$ such that $sgn B = sgn A$ . For a square real matrix $A$ , the Drazin inverse of $A$ is the unique real matrix $X$ such that $A^{k + 1} X = A^{k}$ , $X A X = X$ and $A X = X A$ , where $k$ is the Drazin index of $A$ . We say that $A$ has signed Drazin inverse if $sgn {\tilde{A}}^{d} = sgn A^{d}$ for any $\tilde{A} \in 𝒬 (A)$ , where $A^{d}$ denotes the Drazin inverse of $A$ . In this paper, we give necessary conditions for some block triangular matrices...

Approximating real linear operators

Marko Huhtanen, Olavi Nevanlinna (2007)

Studia Mathematica

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A framework to extend the singular value decomposition of a matrix to a real linear operator $ℳ : ℂ ⁿ \to ℂ^{p}$ is suggested. To this end real linear operators called operets are introduced, to have an appropriate generalization of rank-one matrices. Then, adopting the interpretation of the singular value decomposition of a matrix as providing its nearest small rank approximations, ℳ is approximated with a sum of operets.

On an extension of Fekete’s lemma

Inheung Chon (1999)

Czechoslovak Mathematical Journal

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We show that if a real $n \times n$ non-singular matrix ( $n \geq m$ ) has all its minors of order $m - 1$ non-negative and has all its minors of order $m$ which come from consecutive rows non-negative, then all $m$ th order minors are non-negative, which may be considered an extension of Fekete’s lemma.

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...

New results about semi-positive matrices

Jonathan Dorsey, Tom Gannon, Charles R. Johnson, Morrison Turnansky (2016)

Czechoslovak Mathematical Journal

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Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least $2$ elements is the spectrum of a square semipositive...

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

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Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.

A matrix formalism for conjugacies of higher-dimensional shifts of finite type

Michael Schraudner (2008)

Colloquium Mathematicae

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We develop a natural matrix formalism for state splittings and amalgamations of higher-dimensional subshifts of finite type which extends the common notion of strong shift equivalence of ℤ⁺-matrices. Using the decomposition theorem every topological conjugacy between two $ℤ^{d}$ -shifts of finite type can thus be factorized into a finite chain of matrix transformations acting on the transition matrices of the two subshifts. Our results may be used algorithmically in computer explorations on...

The inertia set of nonnegative symmetric sign pattern with zero diagonal

Yubin Gao, Yan Ling Shao (2003)

Czechoslovak Mathematical Journal

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The inertia set of a symmetric sign pattern $A$ is the set $i (A) = {i (B) ∣ B = B^{T} \in Q (A)}$ , where $i (B)$ denotes the inertia of real symmetric matrix $B$ , and $Q (A)$ denotes the sign pattern class of $A$ . In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern $A$ in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns $A$ with zero diagonal...

Displaying similar documents to “The Re-nonnegative definite solutions to the matrix equation A X B = C ”

Displaying similar documents to “The Re-nonnegative definite solutions to the matrix equation $A X B = C$ ”