Linear Algebra
The fundamental problem of Linear Algebra is solving a System of Linear Equations
- Matrices are the main building blocks of linear algebra
- The easiest way to solve a system is Gaussian Elimination
- its byproduct is LU Decomposition
- A system $A \mathbf x = \mathbf 0$ is called homogeneous
- Matrices form Vector Spaces and have subspaces.
- There are Four Fundamental Subspaces
- Column Space, Row Space, Nullspace and left Nullspace
- each (sub)space have a basis
- by knowing the Rank we can know the dimensionality of these subspaces
Sources
- Linear Algebra MIT 18.06 (OCW)
- Kurosh A.G., A Course in Higher Algebra (in Russian)