|
|
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.
|
|
|
Linear Algebra Education at Secondary School
Řepík, Michal ; Jančařík, Antonín (advisor) ; Bureš, Jiří (referee)
The submitted master thesis called Linear Algebra Education at Secondary School consists of a theoretical and an experimental part. The theoretical one deals with the identification of those linear algebra themes, which appear in the secondary school mathematics curriculum. It follows up with a more detailed look into those topics and proposes ways for further extension of secondary level linear algebra education. The main topics, which are identified in the thesis, are vectors and vector spaces, inner and dot product, systems of linear equations and matrices. The main section of this thesis is the experimental part, which incorporates the conclusions of the first one to design and later realise an online educational course of linear algebra as a part of the Talnet project, which took place in the winter semester of the academic year 2015/2016. The end of this thesis contains assessment of the results of this course.
|
|
|
Linear Algebra Education at Secondary School
Řepík, Michal ; Jančařík, Antonín (advisor) ; Bureš, Jiří (referee)
The submitted master thesis called Linear Algebra Education at Secondary School consists of a theoretical and an experimental part. The theoretical one deals with the identification of those linear algebra themes, which appear in the secondary school mathematics curriculum. It follows up with a more detailed look into those topics and proposes ways for further extension of secondary level linear algebra education. The main topics, which are identified in the thesis, are vectors and vector spaces, inner and dot product, systems of linear equations and matrices. The main section of this thesis is the experimental part, which incorporates the conclusions of the first one to design and later realise an online educational course of linear algebra as a part of the Talnet project, which took place in the winter semester of the academic year 2015/2016. The end of this thesis contains assessment of the results of this course.
|
|
|
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.
|
|
| |
|
| |
guest ::
RSS feed.