Glossary math Term Page

Singular Value Decomposition

A factorization into orthogonal directions and scaling

singular-value-decomposition #math#linear-algebra

Korean version

Aliases

singular value decompositionSVD

Prerequisites

Matrix Orthogonality

Related Concepts

Eigenvalue Rank Projection

Core Idea

Singular value decomposition factors a matrix into orthonormal input directions, scaling magnitudes, and orthonormal output directions. It works for all real or complex matrices, including rectangular ones.

Role In This Blog

In Mathbong, SVD is the final general-purpose decomposition tool that ties together rank, singular values, approximation, compression, and dimensionality reduction.

Posts Mentioning This Concept

[Linear Algebra Series Part 1] A Linear Algebra Roadmap for Programmers See how this 20-part linear algebra series is sequenced for programming, machine learning, graphics, and data work, and why it is ordered this way.[Linear Algebra Series Part 18] Least Squares and the Basics of Linear Regression Use [[least-squares|least squares]] and [[linear-regression|linear regression]] to find the best approximate solution when `Ax = b` has no exact answer.[Linear Algebra Series Part 19] Eigenvalues and Eigenvectors: Directions That Stay Special Under a Transformation Use [[eigenvalue|eigenvalues]] and [[eigenvector|eigenvectors]] to understand special directions of a transformation and connect them to [[pca|PCA]].