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 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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
7
Views
259
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