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pro vyhledávání: '"15A45"'
In this paper, we establish new normal scalar curvature inequalities on a class of austere submanifolds by proving sharper DDVV-type inequalities on associated austere subspaces. We also provide some examples of austere submanifolds in this class and
Externí odkaz:
http://arxiv.org/abs/2410.17761
Autor:
Tripathi, Raghavendra
In a seminal paper in 1959, Marcus and Ree proved that every $n\times n$ bistochastic matrix $A$ satisfies $\|A\|_{\operatorname{F}}^2\leq \max_{\sigma\in S_n}A_{i,\sigma(i)}$ where $S_n$ is the symmetric group on $\{1, \ldots, n\}$. Erd\H{o}s asked
Externí odkaz:
http://arxiv.org/abs/2410.06612
Autor:
Ipsen, Ilse C. F., Saibaba, Arvind K.
We compare the properties of the stable rank and intrinsic dimension of real and complex matrices to those of the classical rank. Basic proofs and examples illustrate that the stable rank does not satisfy any of the fundamental rank properties, while
Externí odkaz:
http://arxiv.org/abs/2407.21594
In this paper, various properties of core-EP matrices are investigated. We introduce the MPDMP matrix associated with $A$ and by means of it, some properties and equivalent conditions of core-EP matrices can be obtained. Also, properties of MPD, DMP,
Externí odkaz:
http://arxiv.org/abs/2407.02602
Autor:
Fanghong, Nan, Zhang, Teng
Byusing equivalence conditions for sectorial matrices obtained by Alakhrass and Sababheh in 2020, we improve a Rotfel'd type inequality for sectorial matrices derived by P. Zhang in 2015 and generalize a result derived by Y. Mao et al. in 2024.
Externí odkaz:
http://arxiv.org/abs/2404.12849
Autor:
Yamada, Akira
In 2012, we obtained Oppenheim's inequality for positive semidefinite matrices and its equality condition by the reproducing kernel method. In this paper, as a continuation, we give a reproducing kernel proof of the block matrix version of the Oppenh
Externí odkaz:
http://arxiv.org/abs/2402.16228
Autor:
Hiai, Fumio
We are concerned with log-majorization for matrices in connection with the multivariate Golden--Thompson trace inequality and the Karcher mean (i.e., a multivariate extension of the weighted geometric mean). We show an extension of Araki's log-majori
Externí odkaz:
http://arxiv.org/abs/2402.16067
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.
Comment: any comments are welcome! Accepted by Advances in Mathematics (China)
Comment: any comments are welcome! Accepted by Advances in Mathematics (China)
Externí odkaz:
http://arxiv.org/abs/2402.01085
Publikováno v:
Acta Sci. Math. (Szeged) (2023)
M. Lin defined a binary operation for two positive semi-definite matrices in studying certain determinantal inequalities that arise from diffusion tensor imaging. This operation enjoys some interesting properties similar to the operator geometric mea
Externí odkaz:
http://arxiv.org/abs/2402.06637
Autor:
Gan, Luyining, Huang, Huajun
On the space of positive definite matrices, several operator means are popular and have been studied extensively. In this paper, we investigate the near order and the L\"owner order relations on the curves defined by the Wasserstein mean and the spec
Externí odkaz:
http://arxiv.org/abs/2312.15394