So what's the point of linear algebra, anyway?(chittur.dev) |
So what's the point of linear algebra, anyway?(chittur.dev) |
Big fan of this approach! Though I have warmed up to determinants ever since I saw 3Blue1Brown give a fairly intuitive explanation for them [0].
I'm kind of curious as to how they covered eigenvalues/the characteristic polynomial without determinants. Maybe they just jumped straight to diagonalization?
If T is a linear operator on vector space V, a scalar a is an eigenvalue if there is a v in V s.t. Tv = av.
This is the approach the book takes.
Av = λv
=> Av - λv = 0
=> (A - λI)v = 0
=> det(A - λI) = 0
If "computation" is what you are after then Av = λv is about solving a system of equations and you can try elimination, etc.