**Linear algebra** is a branch of algebra dealing with the study of vector spaces and the linear transformations inter them. In a more abstract set up **linear algebra** is the category of vector spaces.

## Topics of study

- System of linear equations
- Matrix theory and operations
- Eigenvalues and eigenvectors
- Inner products and inner product spaces
- Linear transformations
- Vector spaces and subspaces

## Applications

Concepts in linear algebra are central in many areas of mathematics, both pure and applied. The precepts of linear algebra form the basis of abstract algebra, and are heavily used in vector calculus, differential equations, analytic geometry, physics, computer science, economics, and engineering.