I was searching for a product symbol like the ordinary $\prod$ but for matrices, where you can specify if the matrix-multiplication should be performed from the right or left. Something like:  $^{R}\prod_{i=1}^{3}M_{i}=M_{1}\cdot M_{2}\cdot M_{3}$  $^{L}\prod_{i=1}^{3}M_{i}=M_{3}\cdot M_{2}\cdot M_{1}$  Does somebody know anything like this? Thanks in advance!  Sebastian
My lecturer has used some notation that I've never seen before: it is a (matrix) product symbol with a left-to-right arrow over the top. Does anybody know what this means?  Thanks in advance.  Edit: It looks like this:
Elements of order 2 in $D_{2n}$ Im new at this abstract algebra stuff and im not comfortable with the proofs techniques yet, so I have a question related to the elements of order $2$ in $D_{2n}$.  Problem:   Prove that $\{x\in D_{2n}|x^{2}=1\}$ is not a subgroup of $D_{2n}$ for $n\geq 3$.   By now, I know that all the elements of the form $sr^{k}$ has order $2$ because I tested by brute force haha, but my real question is how do I prove prove that. How do I have to proceed to prove that $sr^k$ has order 2.  Any help will be really appreciated, thanks so much &lt;3 Reverse of number in PHP not showing correct output Currency formatting in Python I am looking to format a number like 188518982.18 to £188,518,982.18 using Python.  How can I do this? Coming from a java background, one of the things I am used to is telling the JVM what the maximum heap size should be.  If the running program tries to swallow more than is allowed, and the garbage collector cannot free any more resources, then OutOfMemoryError is thrown and it all goes bang.  So setting the maximum heap size is important in Java.  Does this apply in .net?  Can you set the heap size limits?  Does the CLR just keep growing its heap until it reaches the machine's physical limits?  Or is it not an issue in .net for some subtle reason that my Java blinkers stop me from seeing? Can an LC oscillator be used to generate visible light? The LC oscillator is most commonly used to generate radio waves for practical use and the frequency $\omega$ of the LC oscillator equals that of the electromagnetic wave so produced. So, can they in principle be used to emit visible light?  The frequency of visible light is on the order of a few hundred terahertz, and the frequency of an LC oscillator is   $$\omega = \frac{1}{\sqrt{LC}}$$  I admit, the  product $LC$ does become very small (on the order of $10^{-30}$) when the numbers are plugged in, but making an inductor and a capacitor with small values isn't difficult, is it? How to combine various armatures? Last two digits of $3^{400}$ How to learn commutative algebra? Last Logon Time of All Users - RDP server not on a domain From Stewart 7e pg 614 # 9  "One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard th eremor and the fraction who have not hear the rumor. a) Write a differential equation that is satisfied by y. b) Solve the differential equation c) A small town has 1000 inhabitants. At 8 am 80 people have heard a rumor. By noon half the town has heard it. At what will 90 percent of the population have heard the rumor? "  The wording of this is very ambiguous to me and I can't really make sense of it.  They mention a product, so I know that something is being multiplied and that y is a fraction which belongs to the population who have seen it so I think that "have not" heard is a constant, and that y is a fraction taht represents who have. I tried to set this up and it is the wrong answer. I am not sure what they want from that, the English usage is too ambiguous to make sense of it. The complete lack of punctuation is what really does it. Normal Subgroup Counterexample Im having trouble with the second part of this question,  Let $H$ be a normal subgroup of $G$ with $|G:H| = n$,  i) Prove $g^n \in H$ $\forall g \in G$ (which i have done)  ii) Give an example to show that this all false when $H$ is not normal in $G$.(which I am having trouble with showing)  Any suggestions? Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$ Does anyone know how to prove the following:       Suppose $A$ and $B$ are both positive definite and $A - B$ is positive semi-definite.   Show that $B^{-1} - A^{-1}$ is also positive semi-definite.    I really appreciate any comments! Why is the picture not inserted? I am sure there is something wrong i am doing but i just want someone to point it to me.  Why can't we say that $e^{\frac {\pi i}{3}} = \left(e^{\pi i}\right)^{\frac {1}{3}} = (-1)^{\frac {1}{3}} = -1$ Why do we have to calculate it by the formula as it is (which produces different value)  Another question is why can't we say that $ (-1)^{\frac {1}{2}} = \left(\left (-1\right)^{2}\right)^{\frac {1}{4}} = 1^{\frac {1}{4}} = 1$  Again i have to say that i know this is all wrong i just want to know why it is wrong 32-bit vs. 64-bit systems How does Dijkstra's Algorithm and A-Star compare? I'm using the alpha version of the android app on the first generation nexus 7 tablet.  The font size is a little bit small for my liking and I'm not able to pinch zoom to increase the font size.  Is this a feature that is planned in the release? What is the proper way to extend the Fibonacci numbers to negative numbers? I have a feeling this question is a duplicate, but it's not coming up in "Questions that may already have your answer."  We all know very well that $F(0) = 0$, $F(1) = 1$ and $F(n) = F(n - 2) + F(n - 1)$ for all $n &gt; 1$.  I'm wondering about $n &lt; 0$. My first thought was $F(-n) = -F(n)$, which is appealing from a multiplicative point of view, as it seems to preserve certain identities, like $F(n)^2 = F(n - 1) F(n + 1) - (-1)^n$.  But it doesn't quite make sense from an additive point of view, it doesn't seem to work both "forwards" and "backwards." For example, it would give us $F(-1) + F(0) = -1 \neq F(1)$.  How do we extend $F(n)$ to negative $n$ so as to maintain both the related identities and the basic defining identity? Uses of the 3D Cursor How to use variables inside single quotes