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.
doaj +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
core +2 more sources
Linear maps preserving rank 2 on the space of alternate matrices and their applications
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 63, Page 3409-3417, 2004., 2004 Denote by 𝒦n(F) the linear space of all n × n alternate matrices over a field F. We first characterize all linear bijective maps on 𝒦n(F)(n ≥ 4) preserving rank 2 when F is any field, and thereby the characterization of all linear bijective maps on 𝒦n(F) preserving the max‐rank is done when F is any field except for {0, 1} .
Chongguang Cao, Xiaomin Tang
wiley +1 more source
Rank Function Equations and their solution sets [PDF]
, 2013 We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.Comment: 8 pages, all
Pokora, Piotr
core +2 more sources
A hierarchy in the family of real surjective functions
Open Mathematics, 2017 This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties.
Fenoy-Muñoz Mar +3 more
doaj +1 more source