For positive definite matrices A and B, the Kubo-Ando matrix power mean is defined as P?(p,A,B)=A1/2(1+(A?1/2BA?1/2)p2)1/pA1/2(p?0). In this paper, for 0?p?1?q, we show that if one of following inequalities f(P?(p,A,B))?f(P?(1,A,B))?f(P?(q,A,B)) holds any then function f operator monotone on (0,?). We also study inverse problem non-Kubo-Ando means with powers 1/2 2. As a consequence, establish ...

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

The spectral and Jordan structures of the web hyperlink matrix G(c) = cG + (1 − c)ev have been analyzed when G is the basic (stochastic) Google matrix, c is a real parameter such that 0 < c < 1, v is a nonnegative probability vector, and e is the all-ones vector. Typical studies have relied heavily on special properties of nonnegative, positive, and stochastic matrices. There is a unique nonneg...

In the past few years, successive improvements of the asymptotic complexity of square matrix multiplication have been obtained by developing novel methods to analyze the powers of the Coppersmith-Winograd tensor, a basic construction introduced thirty years ago. In this paper we show how to generalize this approach to make progress on the complexity of rectangular matrix multiplication as well,...

To determine the order in which to display web pages, the search engine Google computes the PageRank vector, whose entries are the PageRanks of the web pages. The PageRank vector is the stationary distribution of a stochastic matrix, the Google matrix. The Google matrix in turn is a convex combination of two stochastic matrices: one matrix represents the link structure of the web graph and a se...