Results 31 to 40 of about 543,835 (181)
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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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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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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Geometry of Matrix Polynomial Spaces [PDF]
Foundations of Computational Mathematics, 2019 Let \(P(\lambda)\) be an \(m \times n\) matrix polynomial defined by \[ P(\lambda) = \lambda^d A_d + \dots + \lambda A_1 +A_0 \] where \(A_i \in {\mathbb C} ^{m\times n}\) for \(i = 0, \dots, d\), and \(A_d \neq 0\). Let \(E(\lambda)\) be an \(m\times n\) matrix polynomial with \(\deg P(\lambda) \ge \deg E(\lambda)\).
Dmytryshyn, Andrii +3 more
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The Kalman-Yakubovich-Popov lemma in a behavioural framework [PDF]
, 1997 The classical Kalman-Yakubovich-Popov Lemma provides a link between dissipativity of a system in state-space form and the solution to a linear matrix inequality.
Geest, Robert van der, Trentelman, Harry
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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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MachinesThis paper presents a linear algebra-based control algorithm for multivariable gas turbine systems using matrix polynomial theory and the Kronecker product to assign block roots (i.e., block eigenvectors with prescribed latent structure). State and state-
Belkacem Bekhiti +3 more
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A SURJECTIVITY PROBLEM FOR MATRICES AND NULL CONTROLLABILITY FOR DIFFERENCE AND DIFFERENTIAL MATRIX EQUATIONS [PDF]
Surveys in Mathematics and its Applications, 2020 Let P be a complex polynomial. We prove that the associated polynomial matrix-valued function \tildeP is surjective if for each λ ∈ ℂ the polynomial P-λ has at least a simple zero. The null controllability for difference and differential matrix equations
Donal O'Regan, Constantin Buşe
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