

Linear Algebra(4702205/02)
Summer Term 2017/2018
Detailed information about the Czech version of the course is available on the web page of
General subject information is available in
Hours of Instruction
 Day  Time  Room 
Lecture  Monday  8:15  9:45  EB226 
Discussion  Monday  10:00  11:30  EB226 
Office Hours
Day  Time  Room 
Thursday  11:30  12:30  EA533 
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<at>vsb.cz
office room EA533, tel: 59 732 5870 
Content of the Course
Lectures
 Introductory Lectures: (Course organization) LA00intch.pdf, (Applications) LA_0.ppsx
 Matrix Algebra LA01matricesch.pdf ,
 Systems of Linear Equations LA02linsystch.pdf
 The Inverse of a Matrix LA03inversech.pdf
 Vector Spaces LA04VectorSpacesch.pdf,
 Linear Independence, Basis LA05LinearIndepch.pdf
 Dimension of a Vector Space, Rank LA06DimensionRankch.pdf
 Linear Mapping LA07LinearMappingch.pdf
 Bilinear Forms LA08BilinearFormsch.pdf
 Quadratic Forms LA09QuadraticFormsch.pdf
 Scalar Product, Orthogonality LA10ScalarProductch.pdf
 Determinants LA11Determinantsch.pdf
 Introduction to Spectral Theory LA12Spectrumch.pdf
 Exam Review
Discussions  writing English version of materials is in process
 Complex Numbers LA01cvcomplex.pdf
 Vector algebra LAexen01.pdf , laex_01.pdf
 Matrix Algebra LAexen02.pdf , laex_02.pdf , lacv2.pdf
 Solving Systems of Linear Equations LAexen03.pdf , laex_03.pdf , lacv3.pdf
 The Inverse of a Matrix LAexen04.pdf , lacv4.pdf , laex_04.pdf
 Vector Spaces and Subspaces LAexen05.pdf , lacv5.pdf , laex_05.pdf
 Linear Combinations, Linear Dependence and Independence of Vectors, Basis,
LAexen06.pdf , lacv6.pdf , laex_06.pdf
 Vector Coordinates, Matrix Rank, Rank and Consistency of the System (Frobeni's Theorem),
LAexen07.pdf , lacv7.pdf , laex_07.pdf
 Linear Mapping, Kernel, Range, Matrix of a Linear Mapping,
LAexen08.pdf , lacv8.pdf , laex_08.pdf
 Bilinear and Quadratic Forms, Matrix of a Bilinear or a Quadratic form,
LAexen09.pdf , lacv9.pdf , laex_09.pdf
Klasification of Quadratic Forms, Congruences,
LAexen10.pdf , lacv10.pdf , laex_10.pdf
 Scalar Product, Orthogonality, GramSchmidt Process,
LAexen11.pdf , lacv11.pdf , laex_11.pdf
 Determinants, Cramer Rule,
LAexen12.pdf , lacv12.pdf , laex_12.pdf
 Eigenvalues and Eigenvectors, Characteristic Polynomial, Characteristic Equation, Spectral Decomposition,
lacv13.pdf
Time Line of the Course for the Summer Term 2018
Lectures and Discussions  organized in 14 weeks of the semester
#  Datedd.mm.  Content  Notes 
1.  12.02.  Lecture  canceled  lecturer absence 
Discussion 
2.  19.02.  Lecture  Introductory lecture  Vector, Matrix algebra  
Discussion  Vector and Matrix algebra  
3.  26.02.  Lecture  Systems of Lin. Equations, Gaussian Elimination  
Discussion  Matrix Algebra and Solving Systems of Linear Equations  
4.  05.03.  Lecture  Matrix Inverse, Introduction to Vector Spaces  1st part Homework due, 1st Semester est 
Discussion  Matrix inverse 
5.  12.03.  Lecture  Vector spaces, Linear dependency, Basis  
Discussion  Vector Spaces/Subspaces, Linear combinations  
6.  19.03.  Lecture  Linear Independency/Dependency, Dimension and Rank  On Friday (23.03.)  substituting lecture and discussion on Complex numbers at 9:00 in lectureroom ?? 
Discussion  Linear Dependence/Independence of Vectors, Basis  
7.  26.03.  Lecture  Basis, Dimension, Rank of a matrix  2nd part Homework due, 2nd Semester Test 
Discussion  Basis, Dimension, Rank of a matrix 
8.  02.04.  Lecture  holiday  Eastern  
Discussion 
9.  09.04.  Lecture  Linear Mapping  
Discussion  Linear Mapping  
10.  16.04.  Lecture  Bilinear forms and Quadratic forms  
Discussion  Linear mapping (review), Bilinear forms  
11.  23.04.  Lecture  Quadratic forms  clasification 
3rd part Homework due, 3rd Semester Test 
Discussion  Quadratic forms  clasification 
12.  30.04.  Lecture  Determinants, Cramer's Rule  
Discussion  Determinants, Cramer's Rule  
13.  07.05.  Lecture  Introduction to Spectral Theory of Matrices 
4th part Homework due, 4th Semester Test, Friday (11th of May, at 9:00, in EB226)  substituting tests 
Discussion  Eigenvalues and Eigenvectors of a Matrix 
14.  14.05.  Lecture  Scalar Product, Orthogonality  
Discussion  Scalar Product, Orthogonality, Review  
FinalExam Dates
You need to sign up in IS EDISON for the opened exam term.
#  Datedd.mm.  Room  Time 
1.  Monday 21.05.  EB226  9:00 AM 
2.  Thursday 24.05.  EC1  9:00 AM 
3.  Thursday 07.06.  EC1  9:00 AM 
4.  Tuesday 19.06.  EC2  9:00 AM 
5.  Tuesday 26.06.  will be opened on request of a student 
Homework assignments
 LAhomework18part1.pdf
You are expected to work out the homework by hand  neatly (it must be readable).
You may discuss the problems and verify the results with your 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 purpose of the homework is to provide you with exercises on which you can practise your LA skills and get prepared for the semester tests. If you cheat on homework, you cheat on yourself and you will most likely have difficulties to pass the tests. The homework is to be handed in class or to me in my office (EB533) by the due date. You can also email me the scanned copy of your homework, however only as readable "pdf" file. (I will not accept "gif","doc" or any other electornic formats).
 LAhomework18part2.pdf
The same instructions as to homework part1 do apply. Write neatly and staple together all sheets of your work.
 LAhomework18part3.pdf
Complete assignment is available.
Again, the same instructions as to homework part1 do apply. Write neatly and staple together all sheets of your work.
 LAhomework18part4.pdf
You are supposed to work out the whole assignment, despite of it will not be collected. You are recommended to finish the first 3 chapters before the 4th test.
Homework solutions
 LAhomework18part1solution.pdf
 LAhomework18part2solution.pdf
 LAhomework18part3solution.pdf
 LAhomework18part4solution.pdf
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% of active attendance at lectures and discussions (up to 2 absences allowed).
 Four written tests, 6pts each, minimum 10pts out of 24pts.
If the minimum 10pts is not achieved, a student can retake the tests in the form of one summary test provided he/she gained overall 7,8 or 9pts at the end of the semester. If the retaken test is solved successfully (over 50\%) the total score is 10pts.
 Work out the assigned homework, three up to four parts, together 6pts. No minimum # of points is required.
 To obtain the credit for the course, the minimum of 10pts is necessary. Maximum is 30pts.
 Course is finished by written Final Exam.
English materials and literature:
Useful links:
 WIMS  Linear algebra calculator
 Matrix calculator
 Matrix Row Reducer
 Wolfram Alpha

