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seen Jul 23 at 0:48

Aug
9
comment How do I prove the divergence of this series?
@Didier: Oh yeah, thanks for pointing that out!
Aug
9
comment How do I prove the divergence of this series?
@Asaf: Hmm, that's a good point. If the original problem was with $\frac{1}{\log log n}$, I guess my solution was overkill.
Aug
9
answered How do I prove the divergence of this series?
Jun
8
comment How does the parallelogram law imply the existence of an inner product for a given norm?
Thanks! I'm sorry I didn't find that when I searched for this question.
Jun
7
asked How does the parallelogram law imply the existence of an inner product for a given norm?
May
27
comment Understanding the Schwarz reflection principle
Thanks! That was the statement and construction given by the book, and while I could understand it, I didn't understand why my construction didn't work.
May
27
awarded  Scholar
May
27
comment Understanding the Schwarz reflection principle
Thank you! This was exactly my problem! I had assumed that $f(\overline{z})$ was holomorphic because it was a pretty "nice and simple" function. I just started studying complex analysis, so I had the definition of holomorphic memorized without much intution, but I understand the idea a lot better now!
May
27
accepted Understanding the Schwarz reflection principle
May
27
asked Understanding the Schwarz reflection principle
Jan
31
awarded  Supporter
Jan
16
comment Defining the determinant of linear transformations as multilinear alternating form
Aha thanks! I wonder how I overlooked the linearity of $T$. Hm... but I'm also wondering if this could be done in a way similar to the Steinitz exchange lemma. Suppose we order the $e_i$'s and $f_i$'s so that for all $0 \leq k \leq n$, $f_1, \ldots, f_k, e_{k+1}, \ldots, e_n$ span $V$. Then we could go from $vol(Te_1, \ldots, Te_n)/vol(e_1, \ldots, e_n)$ to $vol(Tf_1, \ldots, Tf_n)/vol(f_1, \ldots, f_n)$, replacing one vector at a time. (And the reason the ratio stays the same is because $T$ is linearity.)
Jan
16
awarded  Student
Jan
16
comment Defining the determinant of linear transformations as multilinear alternating form
Adding one row to another does not change the volume, while multiplying a row by a scalar changes the volume by that scalar factor. So if we go from $e_i$'s to another basis, say $f_i's$, then the ratio $vol(f_1, \ldots, f_n)/vol(e_1, \ldots, e_n)$ is the product of all the scalar multiplications. But I don't see why this is the same as $vol(Tf_1, \ldots, Tf_n)/vol(Te_1, \ldots, Te_n)$
Jan
16
asked Defining the determinant of linear transformations as multilinear alternating form