  This document explores the connections between singular value decomposition
(SVD) and various tensor operations in the context of quantum state
calculations and tensor networks. The relationships between SVD and quantities
such as trace, trace distance, Frobenius norm, and fidelity are examined,
highlighting their similarities and differences. The intuition behind these
mathematical connections is explained, providing insights into the underlying
principles and applications of SVD and tensor operations in quantum physics and
computational mathematics
