Linear algebra

Design principles of algebra for different objects of mathematics. The basis of the course on the theory of matrices, making it possible to present all the material from a single point of view

Read at 2-st semester.
2 hours of lectures per week, seminars

• Badin Andrei Valentinovich
• Ovchinnikov Alexey Vitalevich
• Shishkin Alexander Alexandrovich

1. Matrix. Determinants. Systems of linear equations.
2. Linear, Euclidean and unitary spaces. Linear operators.
3. Quadratic and bilinear forms.
4. Tensors. Group.

1 stream

• Questions to second colloquium (2011-2012)
• The plan of lectures (2009-2010)
• The course program (2009-2010)
• Issues and challenges for the exam (2009-2010)
• Challenges to the overall standings(2009-2010)

2 stream (in brackets indicate the date of the last update of file)

• The tasks of the overall standings (2010.06.06)
• Issues and challenges for the exam (2013.05.28)
• V.V. Kolybasova, N. Ch. Krutitskaya A.V. Ovchinnikov. Jordan form of the matrix of operator (2009.03.10)

Ovchinnikov A.V. lectures

• Lectures on Linear Algebra -1.pdf

3 stream (in brackets indicate the date of the last update of file)

• The tasks of the overall standings (2010.06.06)
• Issues and challenges for the exam (2013.05.28)
• V.V. Kolybasova, N. Ch. Krutitskaya A.V. Ovchinnikov. Jordan form of the matrix of operator (2009.03.10)

Badin A.V. lectures

• All lectures (2012.06.01)
• Seminars about Jordan's form (2013.05.28)
• Lecture 01 (Subspaces of linear spaces; 2013.03.11)
• Lecture 02 (The tensor algebra; 2013.03.11)
• Lecture 03 (General information about the linear operators. The matrix of a linear operator; 2013.03.11)
• Lecture 04 (The eigenvalues ​​and eigenvectors of a linear operator; 2013.03.31)
• Lecture 05 (Bringing the matrix of the linear operator to Jordan form; 2013.04.08)
• Lecture 06 (Linear, bilinear and quadratic forms; 2013.04.15)
• Lecture 07 (Lagrangian method, the law of inertia, Sylvester criterion; 2013.04.29)
• Lecture 08 (Linear Euclidean and linear pseudo-Euclidean spaces; 2013.05.14)