Overview
Linear algebra is a vital area of mathematics that focuses on the study of vectors, matrices, and linear transformations. It provides tools for solving systems of linear equations, which are essential in various fields such as engineering, physics, and economics. Understanding the concepts of vector...
Key Terms
Example: Velocity is a vector because it has both speed and direction.
Example: A 2x2 matrix might look like [[1, 2], [3, 4]].
Example: The determinant of a 2x2 matrix [[a, b], [c, d]] is ad - bc.
Example: In the equation Ax = λx, λ is the eigenvalue.
Example: Rotating a vector in space is a linear transformation.
Example: Using row reduction, you can convert a matrix to its row echelon form.
Related Topics
Vector Spaces
Study of collections of vectors that can be added together and multiplied by scalars.
intermediateLinear Programming
Optimization technique for maximizing or minimizing a linear function subject to constraints.
advancedMatrix Factorization
Decomposing a matrix into a product of matrices to simplify computations.
advancedKey Concepts
VectorsMatricesDeterminantsEigenvalues