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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…
Geoffrey Goodson
It is known that if A∈M n is normal (AA * =A * A ) , then AA￣=A￣A if and only if AA T =A T A. This leads to the question: do both AA￣=A￣A and AA T =A T A imply that A is normal? We give an example to show that this is false when n=4, but we show that it is tr…
Rahul Gupta, Garimella Rama Murthy
Various directions of obtaining novel structured matrices are discussed. A new class of matrices, called “the L-family” matrices are introduced and their properties are studied.
Xiaoning Hao, Pengxiang Ren, Runling An
In this paper, we show that if an injective map on symmetric matrices S n ( C ) satisfies then for all , where f is an injective homomorphism on C , S is a complex orthogonal matrix and A f is the image of A under f applied entrywise .
Ber-Lin Yu
Let S be a nonempty, proper subset of all refined inertias. Then , S is called a critical set of refined inertias for ire ducible sign patterns of order n if is sufficient for any sign pattern A to be refined inertially arbitrary. If no proper subset of S is…
Leonardo Simal Moreira
The cross product in Euclidean space IR 3 is an operation in which two vectors are associated to generate a third vector, also in space IR 3 . This product can be studied rewriting its basic equations in a matrix structure, more specifically in terms of deter…
Dabin Zheng, Heguo Liu
It is well known that the Cayley-Hamilton theorem is an interesting and important theorem in linear algebras, which was first explicitly stated by A. Cayley and W. R. Hamilton about in 1858, but the first general proof was published in 1878 by G. Frobenius, a…
Abdul Mohammed, Musa Balarabe, Abdussamad Tanko Imam
This paper considers rank of a rhotrix and characterizes its properties, as an extension of ideas to the rhotrix theory rhomboidal arrays, introduced in 2003 as a new paradigm of matrix theory of rectangular arrays. Furthermore, we present the necessary and s…
Chi-Ye Wu
A block representation of the BLU factorization for block tridiagonal matrices is presented. Some properties on the factors obtained in the course of the factorization are studied. Simpler expressions for errors incurred at the process of the factorization fo…
Alimohammad Nazari, Sajjad Zia Borujeni
In recent years, a number of preconditioners have been applied to solve the linear systems with Gauss-Seidel method (see [1-7,10-12,14-16]). In this paper we use S l instead of (S + S m ) and compare with M. Morimoto’s precondition [3] and H. Niki’s precondit…
Saeed Karimi
In this paper, a new iterative solution method is proposed for solving multiple linear systems A (i) x (i) =b (i) , for 1≤ i ≤ s, where the coefficient matrices A (i) and the right-hand sides b (i) are arbitrary in general. The proposed method is based on the…
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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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