Differences between revisions 1 and 3 (spanning 2 versions)

MATLAB svd

The svd function calculates the SVD decomposition of any matrix.

Contents

Usage

To solve the problem Ax = b for any size matrix A, try:

[U, S, V] = svd(A);
S_inv = diag(1./diag(S));
x = V * S_inv * U' * b;

This is effectively what pinv does.

To calculate the rank k approximation of a matrix A, try:

[U, S, V] = svd(A);
U_k = U(:, 1:k)
S_k = S(1:k, 1:k)
V_k = V(1:k, :)
A_k = U_k * S_k * V_k'

The original A can be returned by U*S*V'.

-  ⇤ ← Revision 1 as of 2026-02-07 04:54:06 → 
  Size: 469
  Editor: DominicRicottone
  Comment: Initial commit
+   ← Revision 3 as of 2026-02-07 05:11:02 → ⇥
  Size: 686
  Editor: DominicRicottone
  Comment: Add appoximation notes
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-This is effectively what [[MATLAB/Svd|pinv]] does.
+This is effectively what [[MATLAB/Pinv|pinv]] does.

To calculate the rank ''k'' [[LinearAlgebra/LowRankApproximation|approximation]] of a matrix `A`, try:

{{{
[U, S, V] = svd(A);
U_k = U(:, 1:k)
S_k = S(1:k, 1:k)
V_k = V(1:k, :)
A_k = U_k * S_k * V_k'
}}}