Displaying similar documents to “A note on consecutive ones in a binary matrix.”

Intervals of certain classes of Z-matrices

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

Discussiones Mathematicae - General Algebra and Applications

Similarity:

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.

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 [...]

Nonsingularity and P -matrices.

Jiří Rohn (1990)

Aplikace matematiky

Similarity:

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

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....