Hermitian Forms: Definition and Properties

This lecture covers the definition and properties of Hermitian forms, which are applications between complex vector spaces that exhibit specific linearity and symmetry properties. The instructor explains the concept of antilinearity, R-linearity, and sesquilinear forms, providing examples and discussing their applications in vector spaces. The lecture also delves into the notion of sesquilinear forms on complex vector spaces, emphasizing their linearity and antilinearity properties. Additionally, the lecture explores the relationship between Hermitian forms and sesquilinear forms, highlighting their significance in various mathematical contexts.