Is this really correct? I thought it was the other way around? *confused*
i.e that the matrix to change the basis from B to E is the matrix where the columns are given by the vectors of B?
Consider the linear operator T on \mathcal{C}^2 with the matrix
\bmatrix 2 && -3\\3 && 2 \endbmatrix
in the standard basis. With the basis vectors
\frac{1}{\sqrt{2}} \bmatrix i \\ 1 \endbmatrix, \quad \frac{1}{\sqrt{2}} \bmatrix -i \\ 1 \endbmatrix
this operator can be written
\bmatrix 2+3i...
yes I understand that the null space of ST i zero, and that null(T) is a subspace of null(ST), but how can we say that null(S) is a subspace of null(ST) ? I must be doing some kind of faulty thinking :(
Don't understand this reasoning with respect to linear operators.
Let S and T be linear operators on the finite dimensional vector space V. Then assuming the composition ST is invertible, we get
\text{null} \; S \subset \text{null} \; ST
Why is that? I thought hard about it but I simply...
Yes I know that here in Sweden there are twice the amount of women in higher education compared to men. It's probably the same situation in most western countries.
A few more are:
Shankar
Sakurai (modern, not advanded)
Kittel (solid state, thermal physics)
Feynman lectures
Peskin & schroeder
Zee
Zwiebach
MTW, gravitation
Weinberg, the quantum theory of fields
At least in my case, the general trend was the important thing. I had pretty bad grades the first year but by the last year I had top marks only, this made it very easy to get into a top graduate school (in Sweden). Also, grades in relevant subjects seems more important than average grade, at...
I vote for Shankar then. For me it is by far the best text on QM. Easy to read yet more advanced than the standard introductory texts such as Griffiths. If you work through Shankar and understand it all I say you get a very good understanding of QM, including an introduction to path integrals...
I never ever use my notes either. I take notes mainly to stay away (and alert) during classes. And besides, why look up stuff in your notes when the lecturer usually follows a book anyway (hence you can find more detailed info in the book). This of course only applies to undergrad courses (for me)