ALGEBRA AND NUMBER THEORY

On the Schatten norm of a linear map on Euclidean spaces

D. N. Kurochkina

Belarusian State University, Minsk, Belarus

Abstract: We find a connection between the Schatten norm of the linear mapping $\mathcal{A:}V \rightarrow W$ 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 $V$.

Keywords: linear map, Euclidean space, singular values, orthogonal matrix, Jensen's inequality, power means, Hadamard's inequality.

UDC: 512.64

Received: 22.01.2025
Revised: 23.03.2025
Accepted: 23.05.2025