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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…
Raed S. Batahan
The object of this paper is to present a new generalization of the Hermite matrix polynomials by means of the hypergeometric matrix function. An integral representation, differential recurrence relation and some other properties of these generalized forms are…
Abdul Mohammed
This paper presents a new technique for expressing rhotrices in a generalize form. The method involves using multiple array indexes as analogous to matrix expressions, unlike the earlier method in the literature, which can only be functional in a single array…
Morteza Seddighin
We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides information about vectors for which the inequa…
Shinji Miura
A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. Th…
Dariusz Jacek Jakóbczak
Mathematics and computer sciences need suitable methods for numerical calculations of integrals. Classical methods, based on polynomial interpolation, have many weak sides: they are useless to interpolate the function that fails to be differentiable at one po…
Huailei Wang
Based on the geometric theories of vector space, a Cross-Identity theorem is proved for the relationship between the power kernels and power images of linear map on its cyclic subspace. By this result, a new approach of proof is found for the fact that a squa…
Saburou Saitoh
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
Shengbiao Hu
A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G . An H -shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula of counting the number of closed 6-walk…
Artyom M. Grigoryan
This paper describes a new method of QR-decomposition of square nonsingular matrices (real or complex) by the Givens rotations through the unitary discrete heap transforms. This transforms can be defined by a different path, or the order of processing compone…
Yuwang Hu, Wei Jiang
The Cartan invariant matrix for the finite group G 2 (13) of type G 2 over the finite field with 13 elements is determined in this paper.
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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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