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Tensor products of vector spaces
Řepík, Michal ; Jančařík, Antonín (advisor) ; Zhouf, Jaroslav (referee)
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.
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Structure of division rings
Reichel, Tomáš ; Žemlička, Jan (advisor) ; Šaroch, Jan (referee)
This bachelor thesis deals with a theorem and its proof, which allows construction of division ring from cyclic field extension which satisfies certain conditions. The reader is expected to have basic knowledge of linear algebra, ring and module theory. For using this theorem the reader also needs some skills in counting Galois groups. In this work there are also included two basic examples of usage the theorem. During the proof we introduce a structure of tensor product and Brauer group. Powered by TCPDF (www.tcpdf.org)
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Structure of division rings
Reichel, Tomáš ; Žemlička, Jan (advisor) ; Šaroch, Jan (referee)
This bachelor thesis deals with a theorem and its proof, which allows construction of division ring from cyclic field extension which satisfies certain conditions. The reader is expected to have basic knowledge of linear algebra, ring and module theory. For using this theorem the reader also needs some skills in counting Galois groups. In this work there are also included two basic examples of usage the theorem. During the proof we introduce a structure of tensor product and Brauer group. Powered by TCPDF (www.tcpdf.org)
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Tensor products of vector spaces
Řepík, Michal ; Jančařík, Antonín (advisor) ; Zhouf, Jaroslav (referee)
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.
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