javasaurus (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
javasaurus) wrote2006-03-14 02:23 pm
javasaurus) wrote2006-03-14 02:23 pm
(no subject)
How's your linear algebra?
Suppose X is an mxn matrix with linearly independent rows (so they form the basis of a subspace, S), and let y be an n-dimensional vector. Then the projection of y onto S is given by
XT(XXT)-1Xy -- where XT is the transpose of X.
My life would be much easier if I could just accept such statements as fact and move on. But nooooooo.... I have to understand *why* they are true. I don't mean proving the statement, but understanding it. This is one of my gripes about a lot of math texts -- they prove rather than explain.
(yes, after much pencil lead and much coffee, I achieved a sufficient understanding to make me happy)
Suppose X is an mxn matrix with linearly independent rows (so they form the basis of a subspace, S), and let y be an n-dimensional vector. Then the projection of y onto S is given by
XT(XXT)-1Xy -- where XT is the transpose of X.
My life would be much easier if I could just accept such statements as fact and move on. But nooooooo.... I have to understand *why* they are true. I don't mean proving the statement, but understanding it. This is one of my gripes about a lot of math texts -- they prove rather than explain.
(yes, after much pencil lead and much coffee, I achieved a sufficient understanding to make me happy)