Welcome to the Linear Algebra Tutorial! This page is designed to help you understand the fundamental concepts of linear algebra, a branch of mathematics that deals with vector spaces, linear transformations, and matrices.
What is Linear Algebra?
Linear algebra is the branch of mathematics that studies vector spaces, linear transformations, and matrices. It is widely used in various fields such as physics, engineering, computer science, and economics.
Key Concepts
- Vector Spaces: A vector space is a collection of vectors that can be scaled and added together. Examples of vector spaces include Euclidean space, function spaces, and the space of polynomials.
- Linear Transformations: A linear transformation is a function that preserves vector space structure. It maps vectors from one vector space to another.
- Matrices: A matrix is a rectangular array of numbers. Matrices are used to represent linear transformations and solve systems of linear equations.
Examples
- Example 1: The dot product of two vectors is a scalar value that measures the similarity between the vectors.
- Example 2: The determinant of a matrix is a scalar value that determines whether the matrix is invertible.
Further Reading
For more information on linear algebra, you can visit our Linear Algebra Resources page.
Image 1: Vector Space
Image 2: Linear Transformation
Image 3: Matrix