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May
14
accepted Are bounded sequences always strictly less than some fixed number $M$?
May
14
comment Are bounded sequences always strictly less than some fixed number $M$?
ok that totally makes sense, thank you for this answer.
May
14
asked Are bounded sequences always strictly less than some fixed number $M$?
May
9
awarded  Fanatic
May
6
accepted Who was the mathematician who thought “god” was out to get him?
May
6
comment Who was the mathematician who thought “god” was out to get him?
oh ok... well thanks all for clearing that up :)
May
6
comment Who was the mathematician who thought “god” was out to get him?
@Arturo: but how was he an atheist if he was convinced that "God" would not let him die? I mean for him to write the letter, he must have thought that there was a god, right?
May
6
asked Who was the mathematician who thought “god” was out to get him?
Apr
27
accepted How is it shown that a Hermitian matrix will be positive definite?
Apr
26
comment How is it shown that a Hermitian matrix will be positive definite?
Thank you very much, this is the sort of thing I was looking for. So a matrix is positive definite if it is hermitian, finite dimensional(is that what all that $k\leq n$ stuff means?), and the determinant is positive? Other question was about the hint, I tried it and got: $z = \left( \begin{array}{c} |i|^2 \\ -(1)(-i) \end{array}\right) \Rightarrow \overline{z}^{t}A_{1}z = 4$, did I misunderstand the inputs?
Apr
26
comment How is it shown that a Hermitian matrix will be positive definite?
@J.M.: sorry, but I still can't understand your idea... First, I thought I had already worked out the $m=1$ case, right? Second, I don't see where, how, or why to make $a,b,c,d$ evaluate to something manifestly nonpositive... Also when you say quadratic form, you are referring to a specific type of mapping, or just any polynomial with terms of degree 2?
Apr
26
comment How is it shown that a Hermitian matrix will be positive definite?
@J.M. : do I need to show that $a^2 +b^2 +c^2 +d^2 \gt ad -bc$? Do you know how to do this? (Sorry if this is trivial...)
Apr
26
comment How is it shown that a Hermitian matrix will be positive definite?
thank you for this answer, it is good to know that this is a possibility, unfortunately I think this method is still a little too advanced.
Apr
26
comment How is it shown that a Hermitian matrix will be positive definite?
@J.M: as to the definition of positive definite: I think it has so far just been $\alpha$ is positive definite $:\Leftrightarrow \forall v \in V, v\neq 0 : \alpha(v,v) \gt 0$... so pretty basic and we haven't covered how eigenvalues relate to that yet...
Apr
26
comment How is it shown that a Hermitian matrix will be positive definite?
@J.M. : To your previous comment, thank you for the tip! Does something like this look like the right direction? $z = (a+bi, c+di)^t \Rightarrow m(a^2 + b^2) -2(ad-bc) +m(c^2+d^2)$ and since $m(a^2 + b^2) -2(ad-bc) +m(c^2+d^2) \geq 0 \Leftrightarrow m \geq \frac{2(ad-bc)}{a^2 + b^2 +c^2 +d^2}$
Apr
26
asked How is it shown that a Hermitian matrix will be positive definite?
Apr
23
accepted What is the difference between finding a basis for a complex and a real space?
Apr
23
comment What is the difference between finding a basis for a complex and a real space?
Thank you very much!
Apr
23
asked What is the difference between finding a basis for a complex and a real space?
Apr
21
revised Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$?
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