Pairs of k-step reachability and m-step observability matrices
Special Matrices, 2013 Let $V$ and $W$ be matrices of size $ n \times pk$ and $q m \times n $, respectively. A necessary and sufficient condition is given for the existence of a triple $(A,B,C)$ such that $V$ a $k$-step reachability matrix of $(A,B)$ and $W$ an $m$-step ...
Ferrante Augusto, Wimmer Harald K.
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Graph complement conjecture for classes of shadow graphs
Operators and Matrices, 2021 The real minimum semidefinite rank of a graph G , denoted mrR+(G) , is defined to be the minimum rank among all real symmetric positive semidefinite matrices whose zero/nonzero pattern corresponds to the graph G .
Monsikarn Jansrang, S. Narayan
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Independence, infinite dimension, and operators
Moroccan Journal of Pure and Applied Analysis, 2023 In [Appl. Comput. Harmon. Anal., 46 (2019), 664673] O. Christensen and M. Hasannasab observed that assuming the existence of an operator T sending en to en+1 for all n ∈ ℕ (where (en)n∈ℕ is a sequence of vectors) guarantees that (en)n∈ℕ is linearly ...
Idrissi Nizar El, Kabbaj Samir
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Miscellaneous equalities for idempotent matrices with applications
Open Mathematics, 2020 This article brings together miscellaneous formulas and facts on matrix expressions that are composed by idempotent matrices in one place with cogent introduction and references for further study.
Tian Yongge
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Characterizations of the group invertibility of a matrix revisited
Demonstratio Mathematica, 2022 A square complex matrix AA is said to be group invertible if there exists a matrix XX such that AXA=AAXA=A, XAX=XXAX=X, and AX=XAAX=XA hold, and such a matrix XX is called the group inverse of AA.
Tian Yongge
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Enumeration of some matrices and free linear codes over commutative finite local rings
Special Matrices, 2021 Let R be a commutative finite local ring. Two enumeration problems over R are presented. We enumerate the matrices over R with a given McCoy rank and a given number of rows of single unit, and the free linear codes over R which have a given rank and a ...
Sirisuk Siripong
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Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields
Special Matrices, 2021 The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽n×n is defined as ℓ1ℓ2· · · ℓn, where ℓj ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero ...
Dukes Peter J., Martínez-Rivera Xavier
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Group inverse of finite potent endomorphisms on arbitrary vector spaces
, 2020 The aim of this work is to introduce the group inverse of a finite potent endomorphism on an infinite-dimensional vector space that generalizes the notion of group inverse of a square finite matrix. The existence and uniqueness of this inverse is proved,
F. P. Romo
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Searching for degenerate Higgs bosons - A profile likelihood ratio method to test for mass-degenerate states in the presence of incomplete data and uncertainties [PDF]
, 2014 Using the likelihood ratio test statistic, we present a method which can be employed to test the hypothesis of a single Higgs boson using the matrix of measured signal strengths.
David, André +2 more
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On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product
International Journal of Mathematics and Mathematical Sciences, 2004 Some mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method.
Yongge Tian
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