Displaying similar documents to “Infinite divisibility of Smith matrices”

Factorizations for q-Pascal matrices of two variables

Thomas Ernst (2015)

Special Matrices

Similarity:

In this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as follows [...] We also find two different matrix products for [...]

Condition numbers of Hessenberg companion matrices

Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)

Czechoslovak Mathematical Journal

Similarity:

The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...

Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods

Mika Mattila, Pentti Haukkanen (2016)

Special Matrices

Similarity:

Let T = {z1, z2, . . . , zn} be a finite multiset of real numbers, where z1 ≤ z2 ≤ · · · ≤ zn. The purpose of this article is to study the different properties of MIN and MAX matrices of the set T with min(zi , zj) and max(zi , zj) as their ij entries, respectively.We are going to do this by interpreting these matrices as so-called meet and join matrices and by applying some known results for meet and join matrices. Once the theorems are found with the aid of advanced methods, we also...

Determinant and Inverse of Matrices of Real Elements

Nobuyuki Tamura, Yatsuka Nakamura (2007)

Formalized Mathematics

Similarity:

In this paper the classic theory of matrices of real elements (see e.g. [12], [13]) is developed. We prove selected equations that have been proved previously for matrices of field elements. Similarly, we introduce in this special context the determinant of a matrix, the identity and zero matrices, and the inverse matrix. The new concept discussed in the case of matrices of real numbers is the property of matrices as operators acting on finite sequences of real numbers from both sides....

Combinatorial aspects of generalized complementary basic matrices

Miroslav Fiedler, Frank Hall (2013)

Open Mathematics

Similarity:

This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.

Characterization of α1 and α2-matrices

Rafael Bru, Ljiljana Cvetković, Vladimir Kostić, Francisco Pedroche (2010)

Open Mathematics

Similarity:

This paper deals with some properties of α1-matrices and α2-matrices which are subclasses of nonsingular H-matrices. In particular, new characterizations of these two subclasses are given, and then used for proving algebraic properties related to subdirect sums and Hadamard products.

A Theory of Matrices of Real Elements

Yatsuka Nakamura, Nobuyuki Tamura, Wenpai Chang (2006)

Formalized Mathematics

Similarity:

Here, the concept of matrix of real elements is introduced. This is defined as a special case of the general concept of matrix of a field. For such a real matrix, the notions of addition, subtraction, scalar product are defined. For any real finite sequences, two transformations to matrices are introduced. One of the matrices is of width 1, and the other is of length 1. By such transformations, two products of a matrix and a finite sequence are defined. Also the linearity of such product...