Displaying similar documents to “Determinant and Inverse of Matrices of Real Elements”

A Theory of Matrices of Real Elements

Yatsuka Nakamura, Nobuyuki Tamura, Wenpai Chang (2006)

Formalized Mathematics

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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...

Factorizations for q-Pascal matrices of two variables

Thomas Ernst (2015)

Special Matrices

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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 [...]

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

Mika Mattila, Pentti Haukkanen (2016)

Special Matrices

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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...

Nonsingularity and P -matrices.

Jiří Rohn (1990)

Aplikace matematiky

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New proofs of two previously published theorems relating nonsingularity of interval matrices to P -matrices are given.

Condition numbers of Hessenberg companion matrices

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

Czechoslovak Mathematical Journal

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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...

Some Special Matrices of Real Elements and Their Properties

Xiquan Liang, Fuguo Ge, Xiaopeng Yue (2006)

Formalized Mathematics

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This article describes definitions of positive matrix, negative matrix, nonpositive matrix, nonnegative matrix, nonzero matrix, module matrix of real elements and their main properties, and we also give the basic inequalities in matrices of real elements.

Intervals of certain classes of Z-matrices

M. Rajesh Kannan, K.C. Sivakumar (2014)

Discussiones Mathematicae - General Algebra and Applications

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Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.