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Advances in Linear Algebra & Matrix Theory (ALAMT) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of Linear Algebra. All the m…
Haixia Chang
In this paper, we consider a constrained low rank approximation problem: , where E is a given complex matrix, p is a positive integer, and is the set of the Hermitian nonnegative-definite least squares solution to the matrix equation . We discuss the range of…
Achiya Dax
This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank -k approximation of a real m × n matrix, A . This method has important applications in nonnegative matrix factor…
Wensheng Li, Lingyu Wan, Mengtian Yue, Wei Chen, Xuedong Zhang
In this paper, the structure of the non-chain ring Z 15 is studied. The ideals of the ring Z 15 are obtained through its non-units and the Lee weights of elements in Z 15 are presented. On this basis, by the Chinese Remainder Theorem, we construct a unique ex…
Yafei Yang, Yuanfu Shao, Mengwei Li
In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov funct…
Heguo Liu, Honglian Zhang
The rational canonical form theorem is very essential basic result of matrix theory, which has been proved by different methods in the literature. In this note, we provide an effcient direct proof, from which the minimality for the decomposition of the ration…
Achiya Dax
Ky Fan maximum principle is a well-known observation about traces of certain hermitian matrices. In this note, we derive a powerful extension of this claim. The extension is achieved in three ways. First, traces are replaced with norms of diagonal matrices, a…
Balasubramani Prema Rangasamy
To explore the various kind of matrices, matrix multiplication, identity matrix, characteristic equation, minimal polynomial and diagonalization, my paper investigates matrices and algebraic operations defined on them. These matrices may be viewed as rectangu…
Wasim Audeh
A numerical radius inequality due to Shebrawi and Albadawi says that: If A i , B i , X i are bounded operators in Hilbert space, i = 1,2,..., n , and f,g be nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t) = t ( t ∈[0, ∞)), then for…
Achiya Dax
Ky Fan trace theorems and the interlacing theorems of Cauchy and Poincaré are important observations that characterize Hermitian matrices. In this note, we introduce a new type of inequalities which extend these theorems. The new inequalities are obtained fro…
Jean-Francois Niglio
In this article, we wish to expand on some of the results obtained from the first article entitled Projection Theory . We have already established that one-parameter projection operators can be constructed from the unit circle . As discussed in the previous a…
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Advances in Linear Algebra & Matrix Theory (ALAMT) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of Linear Algebra. All the m… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
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