Stępniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the corresponding matrices A² and B², in the sense of the Löwner partial ordering, the star partial ordering,...

The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.

We consider an k x k universal matrix G introduced by Hellwig (1976). We analyze two problems: the nonsingularity of the matrix G and the sign-consistency of the elements of the vector r = (ri) and of the solutrion b = (bi) to the system Gb = r. Obtained results generalize the results presented by Kolupa (1977, 1980).

In this article we present a short history of the MatTriad Conferences, a series of international conferences on matrix analysis and its applications. The name MatTriad originally comes from the phrase Three Days Full of Matrices. The first MatTriad was held in the Mathematical Research and Conference Center of the Institute of Mathematics of the Polish Academy of Sciences in Będlewo, near Poznań, Poland, 3–5 March 2005, and has since then been organized biennially. The 8th MatTriad was held in...

For a given square matrix $A\in {M}_{n}\left(\mathbb{R}\right)$ and the vector $e\in {\left(\mathbb{R}\right)}^{n}$ of ones denote by (A,e) the matrix
⎡ A e ⎤
⎣ ${e}^{T}$ 0 ⎦
This is often called the saddle point matrix and it plays a significant role in several branches of mathematics. Here we show some applications of it in: game theory and analysis. An application of specific saddle point matrices that are hollow, symmetric, and nonnegative is likewise shown in geometry as a generalization of Heron’s formula to give the volume of a general simplex, as well as a conditions...

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