Displaying similar documents to “Some new Properties of Sequence Spaces and Application to the Continued Fractions”

The theory and applications of complex matrix scalings

Rajesh Pereira, Joanna Boneng (2014)

Special Matrices

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We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices. A matrix A is a diagonal scaling of a positive definite matrix M if there exists an invertible complex diagonal matrix D such that A = D*MD and where every row and every column of A sums to one. We look at some of the key properties of complex diagonal scalings and we conjecture that every n by n positive definite matrix has at...

Generalizations of Nekrasov matrices and applications

Ljiljana Cvetković, Vladimir Kostić, Maja Nedović (2015)

Open Mathematics

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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...

Determinant and Inverse of Matrices of Real Elements

Nobuyuki Tamura, Yatsuka Nakamura (2007)

Formalized Mathematics

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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....

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 [...]

New results for EP matrices in indefinite inner product spaces

Ivana M. Radojević (2014)

Czechoslovak Mathematical Journal

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In this paper we study J -EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and J -EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by...