Tensor Products and Symmetric Power

This lecture covers the concept of tensor product, basis in the tensor product space, symmetric power, and exterior power of a vector space. It explains the tensor product of linear maps and provides examples of pure tensors. The lecture also discusses the properties of tensor products, including the basis in the tensor product space and the dual space. Additionally, it explores the universal property of tensor products and the properties of bilinear maps. The lecture concludes with the definition and properties of exterior power, along with examples and applications in linear algebra.