Linear algebra is the branch of mathematics concerning vector spaces and linear transformations between such spaces. It includes the study of lines, planes, and subspaces, as well as the structure of abstract algebraic structures such as vector spaces, vector lattices, and algebras.
Key Concepts
- Vector Spaces: A vector space is a collection of objects called vectors, which may be added together and multiplied by numbers, called scalars.
- Matrices: Matrices are rectangular arrays of numbers used to represent systems of linear equations and transformations.
- Determinants: The determinant of a square matrix is a special scalar value that can be computed from the elements of the matrix.
Applications
Linear algebra is used in many fields, including:
- Computer Graphics: For rendering 3D scenes and animations.
- Physics: To describe the motion of objects and the behavior of forces.
- Machine Learning: To represent and manipulate data in high-dimensional spaces.
Learn More
For further reading, you can explore our Introduction to Linear Algebra.