#Math101 Session 39

Time：Sep. 3, 2026, 15:30-17:30

Location：C-103 East Teaching Building, Chang'an Campus

Speaker：Mr. Sun, Wenhao (Class of 2024)

Title：Inner product spaces and normal operators

Abstract：This opening session on advanced linear algebra first reviews basic concepts of inner product space, with an emphasis on orthogonal (real) and unitary (complex) transformations, which are automorphisms that preserve metric and orthogonality structures and serve as the standard tools for simplifying matrix representations. Then we examine normal operators, encompassing self-adjoint, skew-adjoint, and unitary operators as special cases. We will conclude by outlining the logical roadmap from unitary transformations to various kinds of matrix factorizations, specifically spectral, polar, and singular value decompositions.

（文：申爽/审核：郭千桥）