Linear algebra is the branch of mathematics that studies vector spaces, linear equations, matrices, and linear transformations. It is an essential tool in many fields, including physics, engineering, computer science, and economics.
Basic Concepts
- Vector Space: A vector space is a collection of vectors that can be added together and scaled by numbers (scalars).
- Linear Equations: Linear equations involve variables that are raised to the power of 1 or 0, and they can be written in the form
ax + by = c. - Matrices: A matrix is a rectangular array of numbers, symbols, or expressions.
- Linear Transformations: A linear transformation is a function that preserves linear structure, such as addition and scalar multiplication.
Applications
- Computer Graphics: Linear algebra is used to create 3D models, animations, and simulations.
- Physics: Linear algebra is used to solve problems in mechanics, electricity, and quantum mechanics.
- Economics: Linear algebra is used to analyze markets, optimize resources, and predict trends.
Resources
For more information about linear algebra, please visit our linear algebra tutorials.