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Linear Algebra(470-2205/02)


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

DayTimeRoom
LectureMonday9:00 - 10:30EB130
DiscussionMonday10:45 - 12:15EB229

Office Hours

DayTime
Tuesday10:00 - 11:00
Tuesday12:00 - 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 per-email agreement.


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

  1. (2.6.) Lecture canceled due to lecturer absence
  2. (2.13.)
    1st Lecture
    Course organization LA01-intro-ch.pdf, Applications LA_0.ppsx, Matrix Algebra (first part) LA01-matrices-ch.pdf
    1st Discussion
    Complex Numbers LA01-cv-complex.pdf

  3. (2.20.)
    2nd Lecture
    Matrix Algebra (second part) LA01-matrices-ch.pdf,
    Systems of Linear Equations (first part) LA02-linsyst-ch.pdf
    Discussion
    Vector Algebra laex_01.pdf (czech)
    Matrix Algebra lacv2.pdf (czech), laex_02.pdf (czech)

  4. (2.27.)
    3rd Lecture
    Systems of Linear Equations (second part) LA02-linsyst-ch.pdf
    Discussion
    Solving Systems of Linear Equations lacv3.pdf (czech), laex_03.pdf (czech)

  5. (3.6.)
    4th Lecture
    Inverse of a Matrix LA03-invere-ch.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 LA04-VectorSpaces-ch.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.

  6. (3.13.)
    6th Lecture
    Linear Independence, Basis LA05-LinearIndep-ch.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

  7. (3.20.)
    7th Lecture
    Dimension of a Vector Space, Rank LA06-DimensionRank-ch.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

  8. (3.27.)
    8th Lecture
    Linear Mapping LA07-LinearMapping-ch.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 LA08-BilinearForms-ch.pdf
    Quadratic Forms LA09-QuadraticForms-ch.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

  9. (4.3.) !!! Second part homework due date - extended to Wednesday (5th. April) !!!
    10th Lecture
    Quadratic Forms LA09-QuadraticForms-ch.pdf
    Scalar Product, Orthogonality LA10-ScalarProduct-ch.pdf
    Discussion
    Scalar Product, Orthogonality, Gram-Schmidt Process, lacv11.pdf , laex_11.pdf

  10. (4.10.)
    11th Lecture
    Determinants LA11-Determinants-ch.pdf
    Discussion
    Second test
    Determinants, Cramer Rule, lacv12.pdf , laex_12.pdf

  11. (4.17.)
    Holiday - Eastern

    (4.20.)
    The substituting date scheduled for retaking the semester tests. (9 AM at EB126)

  12. (4.24.) !!! Third part homework due date !!!
    12th Lecture
    Introduction to Spectral Theory LA12-Spectrum-ch.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.

  13. (5.1.)
    Holiday - Svátek práce

  14. (5.8.)
    Holiday - Den osvobození


Content of the Course

Lectures - Summer term 2016 version

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

Discussions - so far unfortunately only the Czech version

  1. Complex Numbers LA01-cv-complex.pdf
  2. Matrix Algebra lacv2.pdf , laex_02.pdf
  3. Solving Systems of Linear Equations lacv3.pdf , laex_03.pdf
  4. The Inverse of a Matrix lacv4.pdf , laex_04.pdf
  5. Vector Spaces and Subspaces lacv5.pdf laex_05.pdf
  6. Linear Combinations, Linear Dependence and Independence of Vectors, Basis, lacv6.pdf , laex_06.pdf
  7. Vector Coordinates, Matrix Rank, Rank and Consistency of the System (Frobeni's Theorem), lacv7.pdf , laex_07.pdf
  8. Linear Mapping, Kernel, Range, Matrix of a Linear Mapping, lacv8.pdf , laex_08.pdf
  9. 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
  10. Scalar Product, Orthogonality, Gram-Schmidt Process, lacv11.pdf , laex_11.pdf
  11. Determinants, Cramer Rule, lacv12.pdf , laex_12.pdf
  12. Eigenvalues and Eigenvectors, Characteristic Polynomial, Characteristic Equation, Spectral Decomposition, lacv13.pdf ,

Homework assignments

  1. LA-homework-part1.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.

  2. LA-homework-part2.pdf
  3. LA-homework-part3.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

  1. LA-homework-part1-solution.pdf
  2. LA-homework-part2-solution.pdf
  3. LA-homework-part3-solution.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:
  1. WIMS - Linear algebra calculator
  2. Matrix calculator
  3. Matrix Row Reducer
  4. Wolfram Alpha


  Upraveno: 14.09.2017