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Geometry and inequalities of geometric mean

Trung Hoa Dinh, Sima Ahsani, Tin-Yau Tam (2016)

Czechoslovak Mathematical Journal

We study some geometric properties associated with the $t$ -geometric means $A ♯_{t} B : = A^{1 / 2} {(A^{- 1 / 2} B A^{- 1 / 2})}^{t} A^{1 / 2}$ of two $n \times n$ positive definite matrices $A$ and $B$ . Some geodesical convexity results with respect to the Riemannian structure of the $n \times n$ positive definite matrices are obtained. Several norm inequalities with geometric mean are obtained. In particular, we generalize a recent result of Audenaert (2015). Numerical counterexamples are given for some inequality questions. A conjecture on the geometric mean inequality regarding $m$ pairs...

Girth and subdominant eigenvalues for stochastic matrices.

Kirkland, S. (2005)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Graph fibrations, graph isomorphism, and PageRank

Paolo Boldi, Violetta Lonati, Massimo Santini, Sebastiano Vigna (2006)

RAIRO - Theoretical Informatics and Applications

PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the...

Displaying 21 – 29 of 29

Geometry and inequalities of geometric mean

Girth and subdominant eigenvalues for stochastic matrices.

Graph fibrations, graph isomorphism, and PageRank

Graphs determined by their (signless) Laplacian spectra.

Graphs whose minimal rank is two.

Graphs whose minimal rank is two: the finite fields case.

Green's relations for stochastic matrices

Group inverse for the block matrix with two identical subblocks over skew fields.

Growth in ${SL}_{3} (ℤ / p ℤ)$

Currently displaying 21 – 29 of 29