On the Schatten norm of a linear map on Euclidean spaces
Abstract
We find a connection between the Schatten norm of the linear mapping A :V → W
of Euclidean spaces of dimensions n and m, respectively, and the power means generated by
the lengths of the images of vectors of the orthonormal basis V.
References
1. Horn R., Johnson Ch. Matrix Analysis. Cambridge, Cambridge University Press, 2014.
2. Maltsev A. I. Fundamentals of Linear Algebra. Moscow, Lan, 2024 (in Russian).
3. Kolmogorov A. N., Petrov A. A., Smirnov Yu. M. One Gauss Formula from Least Squares Theory. Izvestiya Akad. Nauk SSSR. Ser. Mat., 1947, vol. 11, no. 6, pp. 561–566 (in Russian).
4. Maltsev A. I. A Remark on the Paper of A. N. Kolmogorov, A. A. Petrov, and Yu. M. Smirnov. Izvestiya Akad. Nauk SSSR. Ser. Mat., 1947, vol. 11, no. 6, pp. 567–568 (in Russian).
5. Nisnevich L. B., Bryzgalov V. I. On a Problem of N-Dimensional Geometry. UMN, 1953, vol. 8, no. 4(56), pp. 169–172 (in Russian).
Review
For citations:
Kurochkina D.N. On the Schatten norm of a linear map on Euclidean spaces. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(1):15-19. (In Russ.)