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 May6 comment Who was the mathematician who thought “god” was out to get him? oh ok... well thanks all for clearing that up :) May6 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? May6 asked Who was the mathematician who thought “god” was out to get him? Apr27 accepted How is it shown that a Hermitian matrix will be positive definite? Apr26 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? Apr26 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? Apr26 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...) Apr26 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. Apr26 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... Apr26 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 $m(a^2 + b^2) -2(ad-bc) +m(c^2+d^2) \geq 0 \Leftrightarrow m \geq \frac{2(ad-bc)}{a^2 + b^2 +c^2 +d^2}$ Apr26 asked How is it shown that a Hermitian matrix will be positive definite? Apr23 accepted What is the difference between finding a basis for a complex and a real space? Apr23 comment What is the difference between finding a basis for a complex and a real space? Thank you very much! Apr23 asked What is the difference between finding a basis for a complex and a real space? Apr21 revised Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$? deleted 1 characters in body Apr17 revised How to show certain things related to scalar products removed unnecessary ">" caused by blockquote formatting Apr17 accepted How to show certain things related to scalar products Apr17 comment How to show certain things related to scalar products thank you for this answer Apr17 comment How to show certain things related to scalar products thanks for all your help Apr17 comment How to show certain things related to scalar products Thank you for this answer. I think I should be able to manage (3) now. With the geometric interpretation I am still a bit stuck. When you mention those 4 corners of the parallelogram, is each one an ordered pair, like $u= (u_1,u_2)$? Also, is "Pythagoras" written in the problem as a pointer to use the Pythagorean theorem somehow? I just don't know exactly where to apply it, I try to 'extend' the parallelogram horizontally to form right angles, but then the lengths become unclear...