Linear algebra nugget of the day. You can classify a 2d quadratic form without finding eigenvalues. Det tells you if the eigenvalues are the same sign and if det is positive, trace tells you which sign. Exercise: what if det is 0?
-
-
What college courses prepare one to learn this?
-
Linear algebra: but one which does stuff like abstract vector spaces, dual space, inner product. A lot of intros are really matrix algebra, which can conceal the subtleties, so it might well be the second linear algebra course that gets to this.
- 4 more replies
New conversation -
-
-
Otherwise, however, it does matter. In particular, I would point to the theory of principal component analysis in statistics: correlations constitute a quadratic form, not a linear transformation, so PCA implicitly references an isomorphism between a vector space and its dual.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.