dantopa

 52 How is the null space related to singular value decomposition? 29 Will $2$ linear equations with $2$ unknowns always have a solution? 24 How does the SVD solve the least squares problem? 22 Difference between least squares and minimum norm solution 15 What forms does the Moore-Penrose inverse take under systems with full rank, full column rank, and full row rank?

### Reputation (8,810)

 +10 Difference between least squares and minimum norm solution +10 SVD and the columns — I did this wrong but it seems that it still works, why? +10 How is the null space related to singular value decomposition? +10 Let $A$ be an $8 \times 5$ matrix of rank 3, and let $b$ be a nonzero vector in $N(A^T)$. Show $Ax=b$ must be inconsistent.

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### Tags (188)

 375 linear-algebra × 230 69 matrix-decomposition × 11 158 matrices × 123 68 systems-of-equations × 20 158 svd × 59 38 calculus × 40 156 least-squares × 107 33 ordinary-differential-equations × 18 86 pseudoinverse × 40 32 optimization × 12

### Bookmarks (29)

 38 Relationship between eigendecomposition and singular value decomposition 22 Why does SVD provide the least squares and least norm solution to $A x = b$? 20 How does the SVD solve the least squares problem? 18 Geometric interpretations of matrix inverses 9 The SVD Solution to Linear Least Squares / Linear System of Equations