Description:

The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (basis, dimension, inner product spaces, linear transformations) including eigenvalues and eigenvectors. Matrix similarity, orthogonal bases, and bilinear and quadratic forms are also covered.

Contents:

1. Polynomials. Introduction to systems of linear equations and Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Matrices: operations, rank, transpose.
5. Determinant and inverse of a matrix.
6. Structure of solutions of systems of linear equations. Frobenius Theorem.
7. Linear mappings. Matrix of a linear mapping.
8. Free vectors. Dot product and cross product.
9. Lines and planes in 3-dimensional real space.
10. Eigenvalues and eigenvectors of matrices and linear mappings.
11. Similarity of matrices, matrices similar to diagonal matrices.
12. Euclidean space, orthogonalization, orthonormal basis. Fourier basis.
13. Introduction to bilinear and quadratic forms.

Seminar contents:

1. Polynomials. Introduction to systems of linear equations and Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Matrices: operations, rank, transpose.
5. Determinant and inverse of a matrix.
6. Structure of solutions of systems of linear equations. Frobenius Theorem.
7. Linear mappings. Matrix of a linear mapping.
8. Free vectors. Dot product and cross product.
9. Lines and planes in 3-dimensional real space.
10. Eigenvalues and eigenvectors of matrices and linear mappings.
11. Similarity of matrices, matrices similar to diagonal matrices.
12. Euclidean space, orthogonalization, orthonormal basis. Fourier basis.
13. Introduction to bilinear and quadratic forms.

Recommended literature:

1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.
2. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 1997.

https://math.fel.cvut.cz/en/people/vivipaol/LAL2015.pdf

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar