Linear Algebra


1. Vector Spaces. Basis. Dimension. Linear Independence.
2. Linear and Bilinear Functions.
3. Quadratic Forms. Inertial Law.
4. Orthogonal Basis for Symmetric Bilinear Functions.
5. Euclidean Spaces. Gram matrices.
6. Hermition Functions and Spaces.
7. Linear Operators. Eigenspaces.
8. Diagonalization of Symmetric Operators.
9. Polar Decomposition.
10. Jordan Normal Form.


[Ax] S. Axler — Linear Algebra Done Right

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