A note on a conjectured singular value inequality related to a linear map

A Singular Value Inequality Related to a Linear Map

A Generalized Singular Value Inequality for Heinz Means

In this paper we will generalize a singular value inequality that was proved before. In particular we obtain an inequality for numerical radius as follows: begin{equation*} 2 sqrt{t (1-t)} omega(t A^{nu}B^{1-nu}+(1-t)A^{1-nu}B^{nu}) leq omega(t A + (1- t) B), end{equation*} where, $ A $ and $ B $ are positive semidefinite matrices, $ 0 leq t leq 1 $ and $ 0 leq nu leq frac{3}{2}.$

A Note on Singular Value Decomposition∗

This note is intended to summarize the definition, properties, interpretation and applications of Singular Value Decomposition (SVD) described by Strang [?], Shilov [?], Johnson and Wichern [?] and Will [?]. 1 Definition Singular Value Decomposition (SVD) technique decomposes a m × n matrix A into the following factored form :

A note on a graph related to the comaximal ideal graph of a commutative ring

  ‎The rings considered in this article are commutative with identity which admit at least two maximal ideals‎.  ‎This article is inspired by the work done on the comaximal ideal graph of a commutative ring‎. ‎Let R be a ring‎.  ‎We associate an undirected graph to R denoted by mathcal{G}(R)‎,  ‎whose vertex set is the set of all proper ideals I of R such that Inotsubseteq J(R)‎, ‎where J(R) is...

A Singular Value Inequality for Heinz Means

We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.