Results 41 to 50 of about 549,018 (333)
Extensions of the Eneström-Kakeya theorem for matrix polynomials
Special Matrices, 2019 The classical Eneström-Kakeya theorem establishes explicit upper and lower bounds on the zeros of a polynomial with positive coefficients and has been generalized for positive definite matrix polynomials by several authors.
Melman A.
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Marginal Fisher Analysis With Polynomial Matrix Function
IEEE Access, 2022 Marginal fisher analysis (MFA) is a dimensionality reduction method based on a graph embedding framework. In contrast to traditional linear discriminant analysis (LDA), which requires the data to follow a Gaussian distribution, MFA is suitable for non ...
Ruisheng Ran +4 more
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The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field [PDF]
, 2000 Let $M$ be a square matrix and let $p(t)$ be a monic polynomial of degree $n$. Let $Z$ be a set of $n\times n$ matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix in $Z$ such that the product matrix $MZ$ has ...
Joachim Rosenthal +3 more
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Bounding hermite matrix polynomials
Mathematical and Computer Modelling, 2004 The main object under investigation is the family of the Hermite matrix orthogonal polynomials \(\{H_n(x,A)\}_{n\geq 0}\), which depends on the matrix parameter \(A\) having all its eigenvalues in the open right half plane. The main result (Theorem 1) states that \[ \| H_{2n}(x,A)\| \leq \frac{(2n+1)!
Defez, E. +3 more
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Generating Polynomials and Symmetric Tensor Decompositions [PDF]
, 2015 This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.
Nie, Jiawang
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Matrix polynomials with specified eigenvalues
Linear Algebra and its Applications, 2015 This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient matrix. Singular value optimization formulas are derived for these distances facilitating their computation.
Karow, Michael, Mengi, Emre
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Polynomials of small degree evaluated on matrices [PDF]
, 2012 A celebrated theorem of Shoda states that over any field K (of characteristic 0), every matrix with trace 0 can be expressed as a commutator AB-BA, or, equivalently, that the set of values of the polynomial f(x,y)=xy-yx on the nxn-matrix K-algebra ...
Mesyan, Zachary
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Positive semidefinite univariate matrix polynomials [PDF]
Mathematische Zeitschrift, 2018 We study sum-of-squares representations of symmetric univariate real matrix polynomials that are positive semidefinite along the real line. We give a new proof of the fact that every positive semidefinite univariate matrix polynomial of size $n\times n$ can be written as a sum of squares $M=Q^TQ$, where $Q$ has size $(n+1)\times n$, which was recently ...
Hanselka, C., Sinn, R.
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AKCE International Journal of Graphs and Combinatorics, 2019 Semigraph is a generalization of graph. We introduce the concept of energy in a semigraph in two ways, one, the matrix energy Em, as summation of singular values of the adjacency matrix of a semigraph, and the other, polynomial energy Ere, as energy of ...
Gaidhani Y.S. +2 more
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Generalization of numerical range of polynomial operator matrices
Tikrit Journal of Pure Science, 2023 Suppose that is a polynomial matrix operator where for , are complex matrix and let be a complex variable. For an Hermitian matrix , we define the -numerical range of polynomial matrix of as , where .
Darawan Zrar Mohammed, Ahmed Muhammad
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