Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but it also extends these ideas to higher dimensions and abstract spaces.
Basic Concepts
- Vector Spaces: A vector space is a collection of objects called vectors, which may be thought of as arrows in the plane or higher-dimensional space.
- Linear Transformations: A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.
- Matrices: Matrices are rectangular arrays of numbers, used to represent linear transformations.
Applications
Linear algebra has many applications in various fields, including:
- Physics: To describe forces, velocities, and other physical quantities.
- Computer Science: In graphics, machine learning, and data analysis.
- Engineering: To solve systems of linear equations and analyze structures.
For more information about linear algebra, you can read our Introduction to Linear Algebra.
Matrix Operations
Here are some common matrix operations:
- Addition: The sum of two matrices is obtained by adding the corresponding entries.
- Subtraction: The difference of two matrices is obtained by subtracting the corresponding entries.
- Multiplication: The product of two matrices is obtained by multiplying the corresponding entries.
Matrix