Tensor products of vector spaces

TENSOR PRODUCTS OF VECTOR SPACES Bachelor thesis Author: Michal Řepík Department: Department of Mathematics and Mathematical Edu- cation, Faculty of Education, Charles University in Pra- gue Supervisor: RNDr. Antonín Jančařík, Ph.D. Key words: Tensor product, tensor, bilinear map, free vector space, quotient space, change-to-base matrix. Abstract The submitted bachelor thesis called Tensor Products of Vector Spaces deals with general construction of tensor product of two vector spaces over the same field using the technique of linearisation of bilinear maps. This construction is supplemented by a discussion on its alternative ways, and a tensor product of a finite system of vector spaces over the same field is added. The paper also defines a (p, q) tensor in various interconnected ways. Basic operations with tensors are also introduced. The thesis offers a short historical review of tensor calculus as well