[Linear Algebra] The Singular Value Decomposition

The Singular Value Decomposition

example

Theorem.

definition

derivation

Bases for Fundamental Subspaces (+visualizing)

Invertible matrix theorem (추가)

Reduced SVD

pseudoinverse

x̂은 Ax=b의 least-squares solution, smallest length

Application

• least-squares solution
• data analysis (covariance matrix)
• image / sound processing
• etc.