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seen Mar 28 at 23:11

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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Apr
17
revised How to show certain things related to scalar products
removed unnecessary ">" caused by blockquote formatting
Apr
17
accepted How to show certain things related to scalar products
Apr
17
comment How to show certain things related to scalar products
thank you for this answer
Apr
17
comment How to show certain things related to scalar products
thanks for all your help
Apr
17
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...
Apr
17
revised How to show certain things related to scalar products
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Apr
17
comment How to show certain things related to scalar products
@Theo: yeah that was the 'workaround' I was trying out, but now I can go ahead and replace the alphas thanks to what you just taught me.
Apr
17
revised How to show certain things related to scalar products
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Apr
17
comment How to show certain things related to scalar products
@Theo: thank you so much for that! I was trying to figure out why it was such a mess... definitely valuable remarks!
Apr
17
revised How to show certain things related to scalar products
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Apr
17
asked How to show certain things related to scalar products
Apr
17
comment Subtraction and division with integers modulo 3
@Gerry: thanks for the explanation. I had copied that notation from Paul R. Halmos -Linear Algebra Problem Book... But, yeah I will definitely try to avoid using those sorts of fractions in the future.
Apr
17
accepted How do you show this property of a differentiable function given information about the derivative?