Singular Value Decomposition

• Can diagnose or (nearly) solve singular or near-singular systems.

• Used for solving linear least-squares problems.

• Theorem: any m n matrix A can be written:

  • A = UWV T

• where U (m n) & V (n n) are orthogonal and W (n n) is a diagonal matrix.

• Proof: buy a good linear algebra textbook.

Notes: