Abstract
We consider conditions on a matrix A with unit operator (2,1)-norm ensuring the existence of a partition of this matrix into two submatrices with (2,1)-norms close to 1/2.
Similar content being viewed by others
References
B. S. Kashin, “A property of bilinear forms,” Soobshch. Akad. Nauk Gruzin. SSR 97 (1), 29–32 (1980).
B. S. Kashin, “Some properties of matrices of bounded operators from the space \(l_2^n\) into \(l_2^m\),” Izv. Akad. Nauk Armyan. SSR Ser. Mat. 15 (5), 379–394 (1980).
B. S. Kashin, “Lunin’s method for selecting large submatrices with small norm,” Mat. Sb. 206 (7), 95–102 (2015) [Sb. Math. 206 (7), 980–987 (2015)]
A. W. Marcus, D. A. Spielman, and N. Srivastava, “Interlacing families II: Mixed characteristic polynomials and the Kadison—Singer problem,” Ann. of Math (2) 182 (1), 327–350 (2015)
N. Srivastava, Interlacing Families Open Problems, Manuscript (2015), https://math.berkeley.edu/~nikhil/courses/270/open.pdf.
B. S. Kashin, “Decomposing an orthogonal matrix into two submatrices with extremally small (2,1)-norm,” Uspekhi Mat. Nauk 72 (5(437)), 193–194 (2017) [Russian Math. Surveys 72 (5), 971–973 (2017)]
I. V. Limonova, “Decomposing a matrix into two submatrices with smaller (2,1)-norms,” Uspekhi Mat. Nauk 71 (4(430)), 185–186 (2016) [Russian Math. Surveys 71 (4), 781–783 (2016)]
B. S. Kashin and A. A. Saakyan, Orthogonal Series (Izd. AFTs, Moscow, 1999) [in Russian]
Funding
This work was supported by the Government of the Russian Federation (grant no. 14. W03.31.0031).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 1, pp. 53–61.
Rights and permissions
About this article
Cite this article
Kashin, B.S., Limonova, I.V. Decomposing a Matrix into two Submatrices with Extremally Small (2,1)-Norm. Math Notes 106, 63–70 (2019). https://doi.org/10.1134/S000143461907006X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S000143461907006X