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
|Lecture||Thursday||9:00 - 10:30||EB229
|Discussion||Thursday||12:30 - 14:00||EB226
|Monday||9:30 - 11:00||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 per-email agreement.
office room EA533, tel: 59 732 5870
Content of the Course
- Introductory Lectures: (Course organization) LA00-int-ch.pdf, (Applications) LA_0.ppsx
- Matrix Algebra LA01-matrices-ch.pdf ,
- Systems of Linear Equations LA02-linsyst-ch.pdf
- The Inverse of a Matrix LA03-inverse-ch.pdf
- Vector Spaces LA04-VectorSpaces-ch.pdf,
- Linear Independence, Basis LA05-LinearIndep-ch.pdf
- Dimension of a Vector Space, Rank LA06-DimensionRank-ch.pdf
- Linear Mapping LA07-LinearMapping-ch.pdf
- Bilinear Forms LA08-BilinearForms-ch.pdf
- Quadratic Forms LA09-QuadraticForms-ch.pdf
- Scalar Product, Orthogonality LA10-ScalarProduct-ch.pdf
- Determinants LA11-Determinants-ch.pdf
- Introduction to Spectral Theory LA12-Spectrum-ch.pdf
- Exam Review
Discussions - writing of English version of course materials is in process
- Complex Numbers LA01-cv-complex.pdf
- Vector algebra LAex-en-01.pdf , laex_01.pdf
- Matrix Algebra LAex-en-02.pdf , laex_02.pdf , lacv2.pdf
- Solving Systems of Linear Equations LAex-en-03.pdf , laex_03.pdf , lacv3.pdf
- The Inverse of a Matrix LAex-en-04.pdf , lacv4.pdf , laex_04.pdf
- Vector Spaces and Subspaces LAex-en-05.pdf , lacv5.pdf , laex_05.pdf
- Linear Combinations, Linear Dependence and Independence of Vectors, Basis,
LAex-en-06.pdf , lacv6.pdf , laex_06.pdf
- Vector Coordinates, Matrix Rank, Rank and Consistency of the System (Frobeni's Theorem),
LAex-en-07.pdf , lacv7.pdf , laex_07.pdf
- Linear Mapping, Kernel, Range, Matrix of a Linear Mapping,
LAex-en-08.pdf , lacv8.pdf , laex_08.pdf
- 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
- Scalar Product, Orthogonality, Gram-Schmidt Process,
LAex-en-11.pdf , lacv11.pdf , laex_11.pdf
- Determinants, Cramer Rule,
LAex-en-12.pdf , lacv12.pdf , laex_12.pdf
- Eigenvalues and Eigenvectors, Characteristic Polynomial, Characteristic Equation, Spectral Decomposition,
Time Line of the Course for the Summer Term 2019
Lectures and Discussions - organized in 14 weeks of the semester
|1.||14.02.||Lecture||Introductory lecture - Vector, Matrix algebra||
|Discussion||Vector and Matrix algebra||
|3.||28.02.||Lecture|| Systems of Lin. Equations, Gaussian Elimination ||
|Discussion|| Matrix Algebra and Solving Systems of Linear Equations ||
|4.||07.03.||Lecture||Matrix Inverse, Introduction to Vector Spaces||
|Discussion||Matrix inverse||Due date to hand Homework Parts 1, 2
First Semester Test
|5.||14.03.||Lecture||Vector spaces, Linear dependency, Basis||
|Discussion||Vector Spaces/Subspaces, Linear combinations||
|6.||21.03.||Lecture||Linear Independency/Dependency, Dimension and Rank||
|Discussion|| Linear Dependence/Independence of Vectors, Basis||
|7.||28.03.||Lecture||Basis, Dimension, Rank of a matrix ||
|Discussion||Basis, Dimension, Rank of a matrix||
|11.||25.04.||Lecture||canceled||due to deans direction
Exam dates will be set by the end of classes
You need to sign up in IS EDISON for the opened exam term.
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Homework Assignments and Solutions
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).
The same instructions as to homework part-1 do apply. Write neatly and staple together all sheets of your work.
Semester Tests and Solutions
- 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
- WIMS - Linear algebra calculator
- Matrix calculator
- Matrix Row Reducer
- Wolfram Alpha