linear algebra

Linear Algebra is the study of vector spaces and the linear map between them.

Vector

• inner product
• norm
• linear combination
• vector projection

Linear System

Main: system of linear equation

• Gaussian elimination
• LU decomposition
• Cramer’s rule

Matrices

Main: matrices

Operations

Operations

• matrix-vector multiplication
• matrix multiplication
• transpose
• permutation
• inverse

Link to original

Special Types

Circular transclusion detected: Concepts/matrix

Vector Spaces

Main: vector spaces

• span
• basis
• dimension
• four fundamental subspaces

Other Operations and Properties

• similar matrices
• independence
• vector orthogonal projection
• orthogonality
  • Gram-Schmidt process
  • QR decomposition
• Determinant
• Least-Squares Problem
• Cramer’s rule
• Eigenvalues and Eigenvectors
• Positive-definite Matrix
• Singular value decomposition

Matrix Calculus

• Multi-Variable Derivative and Jacobian
• Gradient
• Hessian