Mr. Integral
Math notes/Linear Algebra/SVD and Engineering Computation

Pseudoinverses, Low Rank and Conditioning — Cheat sheet

CHEAT SHEET   ·   FREE

Choose “Save as PDF” in the print dialog.
On this page

Core rule

A+=VΣ+UT,x∗=A+b,κ2(A)=σmax⁡/σmin⁡ for invertible A.A^+=V\Sigma^+U^T,\quad x_*=A^+b,\quad \kappa_2(A)=\sigma_{\max}/\sigma_{\min}\text{ for invertible }A.

Watch for

Small singular values amplify noise. Truncation trades accuracy in the original model for reduced sensitivity.