Linear Algebra(470-2205/02)

Summer Term 2018/2019

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

LectureThursday9:00 - 10:30EB229
DiscussionThursday12:30 - 14:00EB226

Office Hours

Monday9:30 - 11:00EA533

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 per-email agreement.

office room EA533, tel: 59 732 5870

Content of the Course


  1. Introductory Lectures: (Course organization) LA00-int-ch.pdf, (Applications) LA_0.ppsx
  2. Matrix Algebra LA01-matrices-ch.pdf ,
  3. Systems of Linear Equations LA02-linsyst-ch.pdf
  4. The Inverse of a Matrix LA03-inverse-ch.pdf
  5. Vector Spaces LA04-VectorSpaces-ch.pdf,
  6. Linear Independence, Basis LA05-LinearIndep-ch.pdf
  7. Dimension of a Vector Space, Rank LA06-DimensionRank-ch.pdf
  8. Linear Mapping LA07-LinearMapping-ch.pdf
  9. Bilinear Forms LA08-BilinearForms-ch.pdf
  10. Quadratic Forms LA09-QuadraticForms-ch.pdf
  11. Scalar Product, Orthogonality LA10-ScalarProduct-ch.pdf
  12. Determinants LA11-Determinants-ch.pdf
  13. Introduction to Spectral Theory LA12-Spectrum-ch.pdf
  14. Exam Review

Discussions - writing of English version of course materials is in process

  1. Complex Numbers LA01-cv-complex.pdf
  2. Vector algebra LAex-en-01.pdf , laex_01.pdf
  3. Matrix Algebra LAex-en-02.pdf , laex_02.pdf , lacv2.pdf
  4. Solving Systems of Linear Equations LAex-en-03.pdf , laex_03.pdf , lacv3.pdf
  5. The Inverse of a Matrix LAex-en-04.pdf , lacv4.pdf , laex_04.pdf
  6. Vector Spaces and Subspaces LAex-en-05.pdf , lacv5.pdf , laex_05.pdf
  7. Linear Combinations, Linear Dependence and Independence of Vectors, Basis, LAex-en-06.pdf , lacv6.pdf , laex_06.pdf
  8. Vector Coordinates, Matrix Rank, Rank and Consistency of the System (Frobeni's Theorem), LAex-en-07.pdf , lacv7.pdf , laex_07.pdf
  9. Linear Mapping, Kernel, Range, Matrix of a Linear Mapping, LAex-en-08.pdf , lacv8.pdf , laex_08.pdf
  10. Bilinear and Quadratic Forms, Matrix of a Bilinear or a Quadratic form, LAex-en-09.pdf , lacv9.pdf , laex_09.pdf
    Classification of Quadratic Forms, Congruences, LAex-en-10.pdf , lacv10.pdf , laex_10.pdf
  11. Scalar Product, Orthogonality, Gram-Schmidt Process, LAex-en-11.pdf , lacv11.pdf , laex_11.pdf
  12. Determinants, Cramer Rule, LAex-en-12.pdf , lacv12.pdf , laex_12.pdf
  13. Eigenvalues and Eigenvectors, Characteristic Polynomial, Characteristic Equation, Spectral Decomposition, lacv13.pdf

Time Line of the Course for the Summer Term 2019

Lectures and Discussions - organized in 14 weeks of the semester

1.14.02.LectureIntroductory lecture - Vector, Matrix algebra
DiscussionVector and Matrix algebra
2.21.02.Lecturecanceledlecturer absence
3.28.02.Lecture Systems of Lin. Equations, Gaussian Elimination
Discussion Matrix Algebra and Solving Systems of Linear Equations
4.07.03.LectureMatrix Inverse, Introduction to Vector Spaces
DiscussionMatrix inverseDue date to hand Homework Parts 1, 2
First Semester Test
5.14.03.LectureVector spaces, Linear dependency, Basis
DiscussionVector Spaces/Subspaces, Linear combinations
6.21.03.LectureLinear Independency/Dependency, Dimension and Rank
Discussion Linear Dependence/Independence of Vectors, Basis
7.28.03.LectureBasis, Dimension, Rank of a matrix
DiscussionBasis, Dimension, Rank of a matrix
11.25.04.Lecturecanceleddue to deans direction

Final-Exam Dates

Exam dates will be set by the end of classes

You need to sign up in IS EDISON for the opened exam term.


Homework Assignments and Solutions

  1. LA-homework19-part1-complexn.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 practice 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 electronic formats).

  2. LA-homework19-part2-MatrixAlgebra-LinSys.pdf

    The same instructions as to homework part-1 do apply. Write neatly and staple together all sheets of your work.

  3. LA-homework19-part3-InverseSpacesIndependence.pdf
  1. LA-homework19-part1-complexn-solution.pdf
  2. LA-homework19-part2-MatrixAlgebra-LinSys-solution.pdf

Semester Tests and Solutions

  1. LA-Test-119-AB-en.pdf
  2. LA-Test-119-AB-en-solution.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, the student can retake the tests in the form of one summary test, provided he/she gained overall score 7,8 or 9pts by the end of the semester. If the retaken test is passed successfully (over 50\% solved) 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 semester credit for the course, the minimum of 10pts is necessary. Maximum is 30pts.
  • Course is finished by the written Final Exam.

English materials and literature:

  • Lectures slides
  • Your notes from discussions
  • Linear Algebra and Its Applications (4th Edition) by David C. Lay
Useful links:
  1. WIMS - Linear algebra calculator
  2. Matrix calculator
  3. Matrix Row Reducer
  4. Wolfram Alpha

  Upraveno: 09.02.2019