101k views

### How do I exactly project a vector onto a subspace?

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I am not ...
2k views

### Is the least-squares solution unique?

I am looking for a line closest to $(-5, -2)$, $(-2, 0)$, $(-1, 0)$, $(2, 3)$, $(5, 4)$ using the least square solution. So I set the line as $$ax+by+c=0$$ let $a=1$ (where $a$ is not $0$ obviously) ...
3k views

### Pseudo inverse of a singular value decomposition SVD is equal to its “real” inverse for a square matrix?

I was reading this book on numeric linear algebra and it said pseudo inverse of a singular value decomposition (SVD) is equal to it's "real" inverse for a square matrix. It said it is quite clear that ...
1k views

### Roles of $\bf A^TA$ ($\text {A transpose A}$) matrices in orthogonal projection

$\bf A^TA$ forms (or equivalently (?) positive semidefinite matrices, or more particularly, covariance matrices($\bf \Sigma$)) are linked in practice to many operations in which data points are ...