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Last update: RNDr. Jakub Staněk, Ph.D. (14.06.2019)
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Last update: RNDr. Martina Škorpilová, Ph.D. (16.02.2024)
Credit is a necessary and sufficient condition for taking the exam.
Credit exams practical knowledge and skills (numerical procedures, derivation, proving).
A prerequisite for obtaining credit is passing a written test (one regular and two correction terms), which will be written at the end of the semester (one regular and two correction terms).
Another condition for granting the credit is participation in exercises (max. three absences).
More information about credits is available at:
http://www.karlin.mff.cuni.cz/~stepanov/
More information is on the page
http://www.karlin.mff.cuni.cz/~becvar/ |
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Last update: RNDr. Martina Škorpilová, Ph.D. (16.02.2024)
S. Lang: Linear Algebra, Addison-Wesley Publishing Company-Reading, 1966.
I. Satake: Linear Algebra, Marcel Dekker, Inc., New York, 1975.
S. Axler: Linear Algebra Done Right, Springer, New York, 1996. |
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Last update: RNDr. Martina Škorpilová, Ph.D. (16.02.2024)
The exam verifies theoretical knowledge (definitions, theorems), understanding mathematical derivation and proofs, formulation skills (using mathematical symbolism).
Credit is a necessary condition for taking the exam.
The structure of the exam (five questions):
1. definition and examples of defined term (2 points), 2. definitions and examples of defined term (3 points), 3. theorem (2 points), 4. simple proof of the given sentence (3 points) , 5. more difficult proof of the sentence (5 points).
The exam is written (approximaly 60 minutes), it is necessary to obtain at least 9 points (out of maximum 15 points).
The grade is determined by the points obtained for examination: 9-11 (Good), 12-13 (Very Good), 14-15 (Excellent). |
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Last update: RNDr. Martina Škorpilová, Ph.D. (16.02.2024)
Determinants. Basic properties, determinant of a block matrix, the expansion of a determinant under a row and a column, the theorem on multiplication of determinants, adjugate matrix, inverse matrix, Cramer´s rule, rank of a matrix, calculation of determinants; examples.
Similarity, characteristic polynomial of a matrix, eigenvalues and eigenvectors, minimal polynomial of a matrix, Cayley-Hamilton theorem, similarity of matrices, simple Jordan matrix, Jordan matrix, the existence of the Jordan canonical form and the methods of evaluation, eigenvalues of symmetric matrix; examples.
Linear forms and dual space. Matrix and analytical expression of a linear form, dual space, dual basis; examples.
Bilinear forms. Matrix and analytical expression of a bilinear form, vertices, symmetric and antisymmetric forms, polar basis, quadratic forms, bilinear and quadratic form on real spaces, normal basis and normal expression, the law of inertia, signature, classification of forms; examples. |