

Linear Algebra(4702205/02)
Summer Term 2017
Detailed information about this course in Czech language is available on the web page of subject guarantor
Also in
Hours of Instruction
 Day  Time  Room 
Lecture  Monday  9:00  10:30  EB130 
Discussion  Monday  10:45  12:15  EB229 
Office Hours
Day  Time 
Tuesday  10:00  11:00 
Tuesday  12:00  13:00 
In posted times I shall be available in my office for your questions on LA, though I recommend that you let me know by email about your intention to come.
Often some more work duties arise in given times.
I could be available for your questions in some other times too, but after former peremail agreement.
tereza.kovarova<zavináč>vsb.cz
kancelář EA533, tel: 59 732 5870 
Time Line of the Course for the Summer Term 2017
Lectures and Discussions  organized in 14 weeks of the semester
 (2.6.) Lecture canceled due to lecturer absence
 (2.13.)
1st Lecture
Course organization LA01introch.pdf, Applications LA_0.ppsx,
Matrix Algebra (first part) LA01matricesch.pdf
1st Discussion
Complex Numbers LA01cvcomplex.pdf
 (2.20.)
2nd Lecture
Matrix Algebra (second part) LA01matricesch.pdf,
Systems of Linear Equations (first part) LA02linsystch.pdf
Discussion
Vector Algebra laex_01.pdf (czech)
Matrix Algebra lacv2.pdf (czech), laex_02.pdf (czech)
 (2.27.)
3rd Lecture
Systems of Linear Equations (second part) LA02linsystch.pdf
Discussion
Solving Systems of Linear Equations lacv3.pdf (czech), laex_03.pdf (czech)
 (3.6.)
4th Lecture
Inverse of a Matrix LA03inverech.pdf
Discussion
Inverse of a Matrix lacv4.pdf , laex_04.pdf
(3.10.) Friday 9:00  10:30, Substituting Lecture ( room EB129 ), !!! First Homework Due Date !!!
5th Lecture
Vector Spaces LA04VectorSpacesch.pdf
Discussion ( room EB129 )
First test
On Friday March 10th at 10:45 you will be given the first of the two semester tests, that will take about 30 up to 45 min.
Concerning the test content the topics covered are: Complex numbers, Vector and matrix algebra, Solving linear systems, Matrices inverses and simple matrix equations, expressions.
 (3.13.)
6th Lecture
Linear Independence, Basis LA05LinearIndepch.pdf
Discussion
Vector Spaces and Subspaces lacv5.pdf laex_05.pdf
Linear Combinations, Linear Dependence and Independence of Vectors, Basis,
lacv6.pdf , laex_06.pdf
 (3.20.)
7th Lecture
Dimension of a Vector Space, Rank LA06DimensionRankch.pdf
Discussion
Linear Combinations, Linear Dependence and Independence of Vectors, Basis,
lacv6.pdf , laex_06.pdf
Vector Coordinates, Matrix Rank, Rank and Consistency of the System (Frobeni's Theorem),
lacv7.pdf , laex_07.pdf
 (3.27.)
8th Lecture
Linear Mapping LA07LinearMappingch.pdf
Discussion
Vector Coordinates, Matrix Rank, Rank and Consistency of the System (Frobeni's Theorem),
lacv7.pdf , laex_07.pdf
Linear Mapping, Kernel, Range, Matrix of a Linear Mapping,
lacv8.pdf , laex_08.pdf
(3.31.) Friday 9:00  10:30 (Lecture room EB129), Substituting Lecture
9th Lecture
Bilinear Forms LA08BilinearFormsch.pdf
Quadratic Forms LA09QuadraticFormsch.pdf
Discussion
Bilinear and Quadratic Forms, Matrix of a Bilinear or a Quadratic form,
lacv9.pdf , laex_09.pdf
Klasification of Quadratic Forms, Congruences,
lacv10.pdf , laex_10.pdf
 (4.3.) !!! Second part homework due date  extended to Wednesday (5th. April) !!!
10th Lecture
Quadratic Forms LA09QuadraticFormsch.pdf
Scalar Product, Orthogonality LA10ScalarProductch.pdf
Discussion
Scalar Product, Orthogonality, GramSchmidt Process,
lacv11.pdf , laex_11.pdf
 (4.10.)
11th Lecture
Determinants LA11Determinantsch.pdf
Discussion
Second test
Determinants, Cramer Rule,
lacv12.pdf , laex_12.pdf
 (4.17.)
Holiday  Eastern
(4.20.)
The substituting date scheduled for retaking the semester tests. (9 AM at EB126)
 (4.24.) !!! Third part homework due date !!!
12th Lecture
Introduction to Spectral Theory LA12Spectrumch.pdf
Discussion
Eigenvalues and Eigenvectors, Characteristic Polynomial, Characteristic Equation, Spectral Decomposition,
lacv13.pdf ,
(4.28.) Friday 9:00  10:30 (Lecture room EB129), Early Exam Date  due to foreign students requests.
 (5.1.)
Holiday  Svátek práce
 (5.8.)
Holiday  Den osvobození
Content of the Course
Lectures  Summer term 2016 version
 Introductory Lectures: (Course organization) LA01intro.pdf, (Applications) LA_0.ppsx
 Matrix Algebra LA01matrices.pdf ,
 Systems of Linear Equations LA02linsyst.pdf
 The Inverse of a Matrix LA03inverse.pdf
 Vector Spaces LA04VectorSpaces.pdf,
 Linear Independence, Basis LA05LinearIndep.pdf
 Dimension of a Vector Space, Rank LA06DimensionRank.pdf
 Linear Mapping LA07LinearMapping.pdf
 Bilinear Forms LA08BilinearForms.pdf
 Quadratic Forms LA09QuadraticForms.pdf
 Scalar Product, Orthogonality LA10ScalarProduct.pdf
 Determinants LA11Determinants.pdf
 Introduction to Spectral Theory LA12Spectrum.pdf
 Exam Review
Discussions  so far unfortunately only the Czech version
 Complex Numbers LA01cvcomplex.pdf
 Matrix Algebra lacv2.pdf , laex_02.pdf
 Solving Systems of Linear Equations lacv3.pdf , laex_03.pdf
 The Inverse of a Matrix lacv4.pdf , laex_04.pdf
 Vector Spaces and Subspaces lacv5.pdf laex_05.pdf
 Linear Combinations, Linear Dependence and Independence of Vectors, Basis,
lacv6.pdf , laex_06.pdf
 Vector Coordinates, Matrix Rank, Rank and Consistency of the System (Frobeni's Theorem),
lacv7.pdf , laex_07.pdf
 Linear Mapping, Kernel, Range, Matrix of a Linear Mapping,
lacv8.pdf , laex_08.pdf
 Bilinear and Quadratic Forms, Matrix of a Bilinear or a Quadratic form,
lacv9.pdf , laex_09.pdf
Klasification of Quadratic Forms, Congruences,
lacv10.pdf , laex_10.pdf
 Scalar Product, Orthogonality, GramSchmidt Process,
lacv11.pdf , laex_11.pdf
 Determinants, Cramer Rule,
lacv12.pdf , laex_12.pdf
 Eigenvalues and Eigenvectors, Characteristic Polynomial, Characteristic Equation, Spectral Decomposition,
lacv13.pdf ,

Homework assignments
 LAhomeworkpart1.pdf,
You are expected to work out the homework by hand.
You may discuss the problems and verify the results with colleagues, but it is your responsibility to solve all the problems individually and make sure,
that you understand all the operations necessary to obtain the results. The homework is to be handed in a class or to me in my office (EB533) by the due date.
If I am not present in my office, you may drop the homework into the mailbox, that is placed on the wall to the right of the office (EB532) door. If you do so, please write me an email. I do not check the mailbox usually.
 LAhomeworkpart2.pdf
 LAhomeworkpart3.pdf
To work out the other parts of the homework, the same instructions as for the first part do apply. About the due dates see above on the page.
Homework solutions
 LAhomeworkpart1solution.pdf
 LAhomeworkpart2solution.pdf
 LAhomeworkpart3solution.pdf
Tests and solutions
Exam review
Course organization
 Course is instructed in 14 lectures (theoretical lessons) and 14 discussions (practical lessons).
 Requirements to obtain the credit for the course are:
 At least 80% attendance of lectures and discussions (up to 3 absences on lectures, up to 3 absences on discussions).
 Take two written tests, 12pts each, obtain minimum 3pts on each of the tests. One of the tests can be retaken by the end of the course.
 Work out the assigned homework, three parts, 2pts each part, together 6pts. Necessary to obtain minimum 3pts.
 All together to obtain minimum of 10pts is necessary. (Maximum is 30 pts.)
 Course is finished by written Final Exam.
English materials and literature:
Useful links:
 WIMS  Linear algebra calculator
 Matrix calculator
 Matrix Row Reducer
 Wolfram Alpha

