Linear Algebra Least Squares Question

flyingmuskrat
Messages
4
Reaction score
0

Homework Statement



Suppose the columns of A are not independent. How could you find a matrix B so that P=B(BTB)^-1BT does give the projection onto the column space of A? (The usual formula will fail when AT A is not invertible).

T is transpose.

Homework Equations


The Attempt at a Solution



I think this is a thought question or something? Do you rearrange the columns...or just delete the dependent columns? But wouldn't that mess up the answer? Idk I got the rest on my p-set but this one I just have nooo idea. I feel like it's really obvious and I'm just missing it. And it's not gram-schmidt or something because that's the section after.
 
Physics news on Phys.org
how about considering a basis for the column space?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Matrix concept Questions (invertibility, det, linear dependence, span)
Replies
4
Views
1K
Minimize integral using orthogonal basis
Replies
2
Views
1K
Proving statements about matrices | Linear Algebra
Replies
25
Views
3K
Linear Algebra: Question about Inverse of Diagonal Matrices
Replies
6
Views
2K
Linearly independent functions with identically zero Wronskian
Replies
1
Views
1K
[Linear Algebra] Maximal linear independent subset
Replies
3
Views
2K
I How do Tensors "work" in relation to linear algebraic objects?
Replies
6
Views
139
The Maximum Rank of a Matrix B Given AB=0 and A is a Full Rank Matrix
Replies
5
Views
2K
Help with linear algebra: vectorspace and subspace
Replies
15
Views
3K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top