The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Andrii Dmytryshyn - One of the best experts on this subject based on the ideXlab platform.
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Generic Symmetric Matrix polynomials with bounded rank and fixed odd grade
arXiv: Numerical Analysis, 2019Co-Authors: Fernando De Terán, Andrii Dmytryshyn, Froilán M. DopicoAbstract:We determine the generic complete eigenstructures for $n \times n$ complex Symmetric Matrix polynomials of odd grade $d$ and rank at most $r$. More precisely, we show that the set of $n \times n$ complex Symmetric Matrix polynomials of odd grade $d$, i.e., of degree at most $d$, and rank at most $r$ is the union of the closures of the $\lfloor rd/2\rfloor+1$ sets of Symmetric Matrix polynomials having certain, explicitly described, complete eigenstructures. Then, we prove that these sets are open in the set of $n \times n$ complex Symmetric Matrix polynomials of odd grade $d$ and rank at most $r$. In order to prove the previous results, we need to derive necessary and sufficient conditions for the existence of Symmetric Matrix polynomials with prescribed grade, rank, and complete eigenstructure, in the case where all their elementary divisors are different from each other and of degree $1$. An important remark on the results of this paper is that the generic eigenstructures identified in this work are completely different from the ones identified in previous works for unstructured and skew-Symmetric Matrix polynomials with bounded rank and fixed grade larger than one, because the Symmetric ones include eigenvalues while the others not. This difference requires to use new techniques.
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Generic Symmetric Matrix pencils with bounded rank.
arXiv: Spectral Theory, 2018Co-Authors: Fernando De Terán, Andrii Dmytryshyn, Froilán M. DopicoAbstract:We show that the set of $n \times n$ complex Symmetric Matrix pencils of rank at most $r$ is the union of the closures of $\lfloor r/2\rfloor +1$ sets of Matrix pencils with some, explicitly described, complete eigenstructures. As a consequence, these are the generic complete eigenstructures of $n \times n$ complex Symmetric Matrix pencils of rank at most $r$. We also show that these closures correspond to the irreducible components of the set of $n\times n$ Symmetric Matrix pencils with rank at most $r$ when considered as an algebraic set.
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Generic skew-Symmetric Matrix polynomials with fixed rank and fixed odd grade
Linear Algebra and its Applications, 2018Co-Authors: Andrii Dmytryshyn, Froilán M. DopicoAbstract:We show that the set of m×m complex skew-Symmetric Matrix polynomials of odd grade d, i.e., of degree at most d, and (normal) rank at most 2r is the closure of the single set of Matrix polynomials ...
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Generic skew-Symmetric Matrix polynomials with fixed rank and fixed odd grade
arXiv: Rings and Algebras, 2017Co-Authors: Andrii Dmytryshyn, Froilán M. DopicoAbstract:We show that the set of $m \times m$ complex skew-Symmetric Matrix polynomials of odd grade $d$, i.e., of degree at most $d$, and (normal) rank at most $2r$ is the closure of the single set of Matrix polynomials with the certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic $m \times m$ complex skew-Symmetric Matrix polynomials of odd grade $d$ and rank at most $2r$. In particular, this result includes the case of skew-Symmetric Matrix pencils ($d=1$).
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Structure preserving stratification of skew-Symmetric Matrix polynomials
Linear Algebra and its Applications, 2017Co-Authors: Andrii DmytryshynAbstract:We study how elementary divisors and minimal indices of a skew-Symmetric Matrix polynomial of odd degree may change under small perturbations of the Matrix coefficients. We investigate these change ...
Froilán M. Dopico - One of the best experts on this subject based on the ideXlab platform.
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Generic Symmetric Matrix polynomials with bounded rank and fixed odd grade
arXiv: Numerical Analysis, 2019Co-Authors: Fernando De Terán, Andrii Dmytryshyn, Froilán M. DopicoAbstract:We determine the generic complete eigenstructures for $n \times n$ complex Symmetric Matrix polynomials of odd grade $d$ and rank at most $r$. More precisely, we show that the set of $n \times n$ complex Symmetric Matrix polynomials of odd grade $d$, i.e., of degree at most $d$, and rank at most $r$ is the union of the closures of the $\lfloor rd/2\rfloor+1$ sets of Symmetric Matrix polynomials having certain, explicitly described, complete eigenstructures. Then, we prove that these sets are open in the set of $n \times n$ complex Symmetric Matrix polynomials of odd grade $d$ and rank at most $r$. In order to prove the previous results, we need to derive necessary and sufficient conditions for the existence of Symmetric Matrix polynomials with prescribed grade, rank, and complete eigenstructure, in the case where all their elementary divisors are different from each other and of degree $1$. An important remark on the results of this paper is that the generic eigenstructures identified in this work are completely different from the ones identified in previous works for unstructured and skew-Symmetric Matrix polynomials with bounded rank and fixed grade larger than one, because the Symmetric ones include eigenvalues while the others not. This difference requires to use new techniques.
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Generic Symmetric Matrix pencils with bounded rank.
arXiv: Spectral Theory, 2018Co-Authors: Fernando De Terán, Andrii Dmytryshyn, Froilán M. DopicoAbstract:We show that the set of $n \times n$ complex Symmetric Matrix pencils of rank at most $r$ is the union of the closures of $\lfloor r/2\rfloor +1$ sets of Matrix pencils with some, explicitly described, complete eigenstructures. As a consequence, these are the generic complete eigenstructures of $n \times n$ complex Symmetric Matrix pencils of rank at most $r$. We also show that these closures correspond to the irreducible components of the set of $n\times n$ Symmetric Matrix pencils with rank at most $r$ when considered as an algebraic set.
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Generic skew-Symmetric Matrix polynomials with fixed rank and fixed odd grade
Linear Algebra and its Applications, 2018Co-Authors: Andrii Dmytryshyn, Froilán M. DopicoAbstract:We show that the set of m×m complex skew-Symmetric Matrix polynomials of odd grade d, i.e., of degree at most d, and (normal) rank at most 2r is the closure of the single set of Matrix polynomials ...
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Generic skew-Symmetric Matrix polynomials with fixed rank and fixed odd grade
arXiv: Rings and Algebras, 2017Co-Authors: Andrii Dmytryshyn, Froilán M. DopicoAbstract:We show that the set of $m \times m$ complex skew-Symmetric Matrix polynomials of odd grade $d$, i.e., of degree at most $d$, and (normal) rank at most $2r$ is the closure of the single set of Matrix polynomials with the certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic $m \times m$ complex skew-Symmetric Matrix polynomials of odd grade $d$ and rank at most $2r$. In particular, this result includes the case of skew-Symmetric Matrix pencils ($d=1$).
Liu Hong-xia - One of the best experts on this subject based on the ideXlab platform.
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SEVERAL RESULTS ON THE TRACE OF HERMITE POSITIVE DEFINITE Symmetric Matrix
Journal of Mathematics, 2012Co-Authors: Liu Hong-xiaAbstract:Several inequalities for Hermite positive definite Symmetric Matrix trace are studied in this paper.By several existing results in [2-6] and scaling methods,the extreme value theorem,Young inequality and Bernoulli inequality of the trace of Hermite positive definite Matrix are obtained.Also,it finds that many elementary mathematics inequalities can be extended to the case of Hermite positive definite Symmetric Matrix trace.
Yuan Hui-ping - One of the best experts on this subject based on the ideXlab platform.
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QR factorization and algorithm for generalized row(column) Symmetric Matrix
Journal of Computer Applications, 2012Co-Authors: Yuan Hui-pingAbstract:The properties and the QR factorization of generalized row(column) Symmetric Matrix were studied,and some new results were gained.The formula and fast calculating way for the QR factorization of generalized row(column) Symmetric Matrix were obtained,and that formula could dramatically reduce the amount of calculation for QR factorization of generalized row(column) Symmetric Matrix,saved dramatically the CPU time and memory without loss of any numerical precision.Meanwhile,the system parameter estimation was discussed,some results of two paper(ZOU H,WANG D,DAI Q.et al.QR factorization for row or column Symmetric Matrix.Science of China: Series A,2002,32(9): 842-849;LIN X L,JIANG Y L.QR Decomposition and Algorithm for Unitary Symmetric Matrix.Chinese Journal of Computers,2005,28(5):817-822) were generalized,and some mistakes of the latter were corrected.
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Singular Value Decomposition of Row(Column) Symmetric Matrix
Journal of North University of China, 2009Co-Authors: Yuan Hui-pingAbstract:The concept of row(column) transposed Matrix is proposed,and the basic properties of the row(column) transposed Matrix and row(column) Symmetric Matrix are analyzed,which leads to some new results.In addition,the formula of the singular value decomposition of row(column) Symmetric Matrix is given,which makes the calculation easy and accurate,and saves the CPU time and memory dramatically without loss of any numerical precision.
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Full rank factorization and orthogonal diagonal factorization of row (column) Symmetric Matrix
Journal of the University of Shanghai for Science and Technology, 2007Co-Authors: Yuan Hui-pingAbstract:The concept of row (column) transposed Matrix and row (column) Symmetric Matrix is given,their basic property is studied,and the formula for full rank factorization and orthogonal diagonal factorization of row (column) Symmetric Matrix are presented,which can reduce dramatically the amount of calculation and save the CPU time and memory without loss of any numerical precision.
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The Almost Orthogonal Matrix and Almost Symmetric Matrix
Chinese Journal of Engineering Mathematics, 2004Co-Authors: Yuan Hui-pingAbstract:Use of sub-transposed Matrix to have given the concepts of almost orthogonal Matrix and almost (anit-)Symmetric Matrix, and their basic properties and relations is discussed, and many new re- sults have been obtained, orthogonal Matrix and Symmetric Matrix and anit- Symmetric Matrix between of corresponding result have been popularized, especially orthogonal Matrix's Cayley decomposition is extended into almost orthogonal Matrix fields, and various kind orthogonal Matrix and Symmetric ma- trix and generalized inverse Matrix is unified.
Bo Kågström - One of the best experts on this subject based on the ideXlab platform.
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Orbit closure hierarchies of skew-Symmetric Matrix pencils
SIAM Journal on Matrix Analysis and Applications, 2014Co-Authors: Andrii Dmytryshyn, Bo KågströmAbstract:We study how small perturbations of a skew-Symmetric Matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-Symmetric Matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-Symmetric Matrix pencil contains the congruence orbit (or bundle) of another skew-Symmetric Matrix pencil. The developed theory relies on our main theorem stating that a skew-Symmetric Matrix pencil $A-\lambda B$ can be approximated by pencils strictly equivalent to a skew-Symmetric Matrix pencil $C-\lambda D$ if and only if $A-\lambda B$ can be approximated by pencils congruent to $C-\lambda D$.
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Orbit closure hierarchies of skew-Symmetric Matrix pencils
SIAM Journal on Matrix Analysis and Applications, 2014Co-Authors: Andrii Dmytryshyn, Bo KågströmAbstract:We study how small perturbations of a skew-Symmetric Matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-Symmetric Matrix ...
