Comments on: Ky Fan Norms, Schatten Norms, and Everything In Between http://www.nathanieljohnston.com/2009/08/ky-fan-norms-schatten-norms-and-everything-in-between/ A blog of recreational math and quantum information theory Mon, 30 Aug 2010 23:33:04 +0000 hourly 1 http://wordpress.org/?v=3.0.1 By: ChapterZero » Spectral spread of Graphs http://www.nathanieljohnston.com/2009/08/ky-fan-norms-schatten-norms-and-everything-in-between/#comment-119 ChapterZero » Spectral spread of Graphs Sat, 31 Jul 2010 00:05:34 +0000 http://www.nathanieljohnston.com/?p=600#comment-119 [...] July 2010 arXiv paper on the application of Ky Fan norms to graphs poses, among others, the following question: what is the maximal spectral spread of a [...] [...] July 2010 arXiv paper on the application of Ky Fan norms to graphs poses, among others, the following question: what is the maximal spectral spread of a [...]

]]> By: Nathaniel http://www.nathanieljohnston.com/2009/08/ky-fan-norms-schatten-norms-and-everything-in-between/#comment-118 Nathaniel Sun, 25 Jul 2010 18:04:47 +0000 http://www.nathanieljohnston.com/?p=600#comment-118 @Yogendra -- Brilliant, thank you! @Yogendra — Brilliant, thank you!

]]> By: Yogendra Chaubey http://www.nathanieljohnston.com/2009/08/ky-fan-norms-schatten-norms-and-everything-in-between/#comment-117 Yogendra Chaubey Sun, 25 Jul 2010 16:04:45 +0000 http://www.nathanieljohnston.com/?p=600#comment-117 In answer to your question "So why have I never seen the natural generalization of these two families of norms — the vector p-norm of the first k singular values — defined?" please see the following references; Mudholkar et al, (1984): J. Math. Anal. and Appl., 102, 435-441. Li, Chi-Kwong; Tsing, Nam-Kiu(1988) Some isometries of rectangular complex matrices. Linear and Multilinear Algebra 23 (1988), no. 1, 47--53.{MR0943768 (89g:15031)} Friemer and Mudholkar (1985) A CLASS OF GENERALIZATIONS OF HOLDER'S INEQUALITY, In Inequalities in Statistics and Applications, IMS In answer to your question “So why have I never seen the natural generalization of these two families of norms — the vector p-norm of the first k singular values — defined?” please see the following references;

Mudholkar et al, (1984): J. Math. Anal. and Appl., 102, 435-441.

Li, Chi-Kwong; Tsing, Nam-Kiu(1988)
Some isometries of rectangular complex matrices.
Linear and Multilinear Algebra 23 (1988), no. 1, 47–53.{MR0943768 (89g:15031)}

Friemer and Mudholkar (1985) A CLASS OF GENERALIZATIONS OF HOLDER’S INEQUALITY, In Inequalities in Statistics and Applications, IMS

]]> By: Nathaniel Johnston » No Similarity-Invariant Matrix Norm http://www.nathanieljohnston.com/2009/08/ky-fan-norms-schatten-norms-and-everything-in-between/#comment-116 Nathaniel Johnston » No Similarity-Invariant Matrix Norm Fri, 04 Sep 2009 12:16:38 +0000 http://www.nathanieljohnston.com/?p=600#comment-116 [...] are weakly unitarily-invariant, including the operator norm, Frobenius norm, numerical radius, Ky Fan norms and Schatten p-norms. One might naturally wonder whether there are matrix norms that satisfy the slightly stronger [...] [...] are weakly unitarily-invariant, including the operator norm, Frobenius norm, numerical radius, Ky Fan norms and Schatten p-norms. One might naturally wonder whether there are matrix norms that satisfy the slightly stronger [...]

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