## Description

This is a page of my course for $1^{st}$ year students of Master’s Program “Advanced Combinatorics” at MIPT.

## Program

- Vector Spaces. Basis. Dimension. Linear Independence.
- Linear and Bilinear Functions.
- Quadratic Forms. Inertial Law.
- Orthogonal Basis for Symmetric Bilinear Functions.
- Euclidean Spaces. Gram matrices.
- Hermition Functions and Spaces.
- Linear Operators. Eigenspaces.
- Diagonalization of Symmetric Operators.
- Polar Decomposition.
- Jordan Normal Form.

## Seminars & Problems

Seminar 1. 06.11.2017. Affine and Vector Spaces.

Seminar 2. 13.11.2017. Transformation Groups.

Seminar 3. 04.12.2017. Linear and Bilinear Functions.

Seminar 4. 11.12.2017. Quadratic Forms and Symmetric Bilinear Functions.

Seminar 5. 08.01.2018. Euclidean and Hermition Spaces.

Seminar 6. 24.01.2018. Linear Operators.

## Seminar Results

See tables

## References

[Ax] S. Axler — Linear Algebra Done Right

[Vi] E.B. Vinberg — Course of Algebra, 2017, MCCME, Moscow.