Displaying similar documents to “Basic Properties of Circulant Matrices and Anti-Circular Matrices”

Generalizations of Nekrasov matrices and applications

Ljiljana Cvetković, Vladimir Kostić, Maja Nedović (2015)

Open Mathematics

Similarity:

In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already...

Some Basic Properties of Some Special Matrices. Part III

Xiquan Liang, Tao Wang (2012)

Formalized Mathematics

Similarity:

This article describes definitions of subsymmetric matrix, anti-subsymmetric matrix, central symmetric matrix, symmetry circulant matrix and their basic properties.

A new characterization of generalized complementary basic matrices

Miroslav Fiedler, Frank J. Hall (2014)

Special Matrices

Similarity:

In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases.

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 [...]

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.

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...