🖥️
Matrix Factorization
★★★★☆Undergraduate
📖Definition
Matrix factorization expresses a matrix as product of simpler matrices. Used for solving systems, eigenvalue computation, and data compression.
📐Formulas
A = LU
LU decomposition (lower × upper triangular)
A = QR
QR decomposition (orthogonal × upper triangular)
A = UΣ Vᵀ
Singular Value Decomposition (SVD)
A = LDLᵀ
Cholesky decomposition (symmetric positive definite)
✏️Examples
예제 1
Explain how to solve Ax = b using LU decomposition.
⚡Applications
Numerical Linear Algebra
Solving linear systems
Machine Learning
Dimensionality reduction, recommender systems
Image Processing
Compression, denoising
🔗Related Documents
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#행렬분해#LU#SVD#matrix factorization