Sketching as a Tool for Numerical Linear Algebra
... Solving least squares regression via the normal equations How to find the solution x to minx |Ax-b|2 ? Equivalent problem: minx |Ax-b |22 Write b = Ax’ + b’, where b’ orthogonal to columns of A Cost is |A(x-x’)|22 + |b’|22 by Pythagorean theorem Optimal solution x if and only if AT(Ax-b) = ...
... Solving least squares regression via the normal equations How to find the solution x to minx |Ax-b|2 ? Equivalent problem: minx |Ax-b |22 Write b = Ax’ + b’, where b’ orthogonal to columns of A Cost is |A(x-x’)|22 + |b’|22 by Pythagorean theorem Optimal solution x if and only if AT(Ax-b) = ...
Subspaces, Basis, Dimension, and Rank
... 1. The row space of A is the subspace row(A) of Rn spanned by the rows of A. 2. The column space of A is the subspace col(A) of Rm spanned by the columns of A. If we need to determine if ~b belongs to col(A), this is actually the same problem as whether ~b ∈ span of the columns of A; see the method ...
... 1. The row space of A is the subspace row(A) of Rn spanned by the rows of A. 2. The column space of A is the subspace col(A) of Rm spanned by the columns of A. If we need to determine if ~b belongs to col(A), this is actually the same problem as whether ~b ∈ span of the columns of A; see the method ...