>Some more question about linear algebra: how do you know when to form a matrix >by inserting into the columns and when to form one by inserting into rows?
I think you're way out of line, mathematically speaking: "Insert into the columns"... You have to get used to a more formal and precise language.
> >Can someone please explain how images, kernels, isomorphisms, and the dimension >theorem relate? > >And what's diagonizability? I know the A-(lambda*I) thing, and then the
"thing" See my comments above.
>determinant of that is the "characteristic polynomial" of the matrix. But how >does that determine diagonizability? > >Also, if det (A) = 0, then the matrix isn't invertible. This means NOTHING >times A can equal I, right?
"Nothing times A": You're not going anywhere. I just *see* strokes of fat red ink on you're paper. Sorry, to be so harsh. Thomas