Linear Algebra: Problems and Methods

Nikolay Gusev Paolo Bonicatto Stefano Modena

Stepic.org

The goal of the course is explain the fundamental ideas of linear algebra and how to use them to find easy solutions of hard problems

Программа

1. Linear Spaces

1.1 Welcome to the Linear Algebra course at Stepic
1.2 Concept of linear space
1.3 Coordinates of vectors and linear maps
1.4 Systems of linear equations
1.5 Structure of linear spaces
1.6 Lesson by Emil Wiedemann
1.7 Quick reference

2. Subspaces

2.1 Span and other subspaces
2.2 Operations with subspaces
2.3 Rank of a matrix
2.4 Operations with matrices

3. Linear Transformations

3.1 Permutations
3.2 Determinants
3.3 Change of basis
3.4 Invariant subspaces

4. Inner Product Spaces

4.1 Eigenvectors, eigenspaces and structure of linear operators
4.2 Inner product spaces and orthogonalization
4.3 Adjoint maps and self-adjoint operators
4.4 Bilinear and quadratic forms

5. Advanced topics I

5.1 Decompositions of matrices (QR, SVD, LU)
5.2 Jordan normal form and Cayley–Hamilton theorem
5.3 Tensors

6. Advanced topics II

6.1 Introduction to numerical mathematics
6.2 Simplex method
6.3 Problems for practice and fun

Ключевые слова

Высшая математика
Линейная алгебра