Overview
Matrix decomposition techniques are essential tools in linear algebra that simplify complex matrix operations. By breaking down matrices into simpler components, these techniques enable easier analysis and solution of linear equations. LU, QR, and SVD are among the most commonly used methods, each w...
Key Terms
Example: A 2x3 matrix has 2 rows and 3 columns.
Example: LU decomposition breaks a matrix into lower and upper triangular matrices.
Example: For matrix A, LU decomposition gives A = L * U.
Example: For matrix A, QR decomposition gives A = Q * R.
Example: For matrix A, SVD gives A = U * Σ * Vᵀ.
Example: In a lower triangular matrix, all elements above the diagonal are zero.
Related Topics
Eigenvalues and Eigenvectors
Study of eigenvalues and eigenvectors, which are crucial in understanding matrix transformations.
intermediateLinear Transformations
Exploration of how matrices can represent linear transformations in vector spaces.
intermediatePrincipal Component Analysis
A statistical technique that uses SVD for dimensionality reduction in data analysis.
advancedKey Concepts
LU DecompositionQR DecompositionSingular Value DecompositionCholesky Decomposition