Activity for Peter Taylor
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #286398 | Initial revision | — | over 2 years ago |
| Question | — |
Matrices with rotational symmetry I've seen a claim without proof that the characteristic polynomials of matrices with rotational symmetry (i.e. $n \times n$ matrices $A$ with $A{i,j} = A{n+1-i,n+1-j}$) always factor into the product of the characteristic polynomials of smaller matrices which can be derived from blocks of the origina... (more) |
— | over 2 years ago |
| Comment | Post #286034 |
@#53398, I'm not sure I get it either. If we have a rotation in a plane around the origin which, applied twice, takes us from $(1,0,0)$ to $(-1,0,0)$ then the plane must contain the origin, the start point, and the end point. By symmetry the square roots of $-1$ end up all being in the plane through ... (more) |
— | over 2 years ago |
| Comment | Post #286188 |
On the subject of having no idea how to answer a question, it's always a good starting point to write it out in terms of the definitions. So "the expected time until the buffer reaches its capacity for the first time" is a weighted sum of probabilities, and the question largely reduces to calculating... (more) |
— | over 2 years ago |
| Comment | Post #286188 |
This site uses a markup tool called MathJax which would improve the legibility of your question considerably. If you surround each formula/expression with dollar signs, you can use underscores `_` to create subscripts, carets `^` to create superscripts, curly brackets `{}` to group subscripts or supe... (more) |
— | over 2 years ago |
| Comment | Post #286166 |
Rather than thinking about going "out of 3D space", it may be helpful to think about it as working with the surface of a 3D unit hypersphere embedded in a 4D space. (more) |
— | over 2 years ago |
| Edit | Post #286130 |
Post edited: MathJaxify, trim some extraneous verbiage |
— | over 2 years ago |
| Edit | Post #286004 | Question closed | — | over 2 years ago |
| Comment | Post #286004 |
Which skewness and which sample skewness? There seem to be multiple, subtly different, parameters with those names. (more) |
— | over 2 years ago |
| Edit | Post #285984 |
Post edited: |
— | almost 3 years ago |
| Comment | Post #285984 |
Quaternions are not complex numbers. The complex numbers can be seen as a subalgebra, but I'm not sure to what extent that is useful or helpful. (more) |
— | almost 3 years ago |
| Edit | Post #285988 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How to write the big Xi notation in MathJax? $\Xi$ may not be what you want, but (a) it's the correct answer to the question as stated; (b) I can't understand why you'd complain that the font used is more legible than a handwritten example deliberately chosen to be difficult to parse. $$\frac{\Xi}{\overline{\Xi}}$$ isn't marvellous, but it's ce... (more) |
— | almost 3 years ago |
| Edit | Post #285682 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How can a 15 year old construe the LHS of Generalized Vandermonde's Identity, when it lacks summation limits and a summation index? You can rewrite it in different notation with sum limits if you want. You just need to use a different way to express the constraint on which terms to include in the sum. E.g. with the Iverson bracket notation the LHS becomes $$\sum{k1 = 0}^m \sum{k2 = 0}^m \cdots \sum{kp = 0}^m [k1+\cdots +kp = m... (more) |
— | almost 3 years ago |
| Edit | Post #285679 | Question closed | — | almost 3 years ago |
| Edit | Post #285674 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: Why 1. multiply the number of independent options? 2. add the number of exclusive options? You might find it more helpful to instead consider only two choices at a time and draw a grid: | beef | chicken | fish | ------+---------+---------+---------+ | beef | chicken | fish | fries | + | + | + | | fries | fries |... (more) |
— | almost 3 years ago |
| Edit | Post #285672 | Question closed | — | almost 3 years ago |
| Comment | Post #285671 |
Have you drawn a diagram of the squares in question? (more) |
— | almost 3 years ago |
| Comment | Post #285015 |
@#55022, if you have a property which you do not find intuitive or counter-intuitive then you need a very good reason for believing that it *should be* intuitive to justify the question. Axioms and definitions are chosen and become popular because they're *useful*, with no guarantees about how intuit... (more) |
— | almost 3 years ago |
| Edit | Post #285527 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How's it possible to arrange 0 objects? How can 0! = 1? Combinatorics is not necessarily tangible, so the question of what it means to physically rearrange objects is irrelevant. On the other hand, it's easy to write down the permutations of small finite numbers of objects: 0: [] 1: [1] 2: [1,2] [2,1] 3: [1,2,3] [1,3,2] [2,1,3] [2,3,... (more) |
— | almost 3 years ago |
| Edit | Post #285476 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: If C = Calvin wins the match, and $X \thicksim Bin(2, p) =$ how many of the first 2 games he wins — then why P(C|X = 1) = P(C)? The key is > the first player to win two games more than his opponent wins the match $P(C \mid X = 1)$ describes the situation when Calvin has won 1 of the first two matches: so the opponent won the other match, and they're currently even. Since a 1-1 score is equivalent to a 0-0 score for the ... (more) |
— | almost 3 years ago |
| Edit | Post #285344 | Question closed | — | almost 3 years ago |
| Comment | Post #285425 |
My impression (and I haven't just rechecked the question list to validate it) is that very few of the questions are at a level of needing a grad student to answer them. It's probably fair to say that those which *are* at that level are mostly unanswered, but it's also probably fair to say that that *... (more) |
— | almost 3 years ago |
| Comment | Post #285342 |
Closed as off-topic because the issue at heart here isn't mathematics but linguistics. In particular, what a good answer would address is the flaws in assuming firstly that a word has only one meaning, and secondly that whoever made that YouTube video is the absolute authority on what that meaning is... (more) |
— | almost 3 years ago |
| Edit | Post #285342 | Question closed | — | almost 3 years ago |
| Comment | Post #285086 |
I don't think that MCD is "based on" either site, but my point is that its scope is similar to MSE's and so it's not a surprise that it has the same problems as MSE. (more) |
— | almost 3 years ago |
| Edit | Post #285086 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How can we grow this community? Certainly low quality content is an issue. Being brutally honest, if I understood the rôle of moderator as being a ruthless dictator who pursues quality above all else I would delete 95% of the questions. But to put that in context, it's also true for most maths fora. I recently saw someone mention a... (more) |
— | almost 3 years ago |
| Comment | Post #284996 |
That graphic helps a lot, thanks. But if the two initial squares aren't horizontally or vertically adjacent, it's not clear that the border is well defined. You can draw the 8-square box around each one, and then connect appropriate corners of the boxes with straight lines, but deciding which squares... (more) |
— | almost 3 years ago |
| Comment | Post #284996 |
The notation can be read "the set of points $(0, t)$ where the variable $t$ is between $0$ and $1$ inclusive". It's just the line segment (technically not a line, because lines are infinite) between the two points. (more) |
— | almost 3 years ago |
| Comment | Post #284996 |
This seems to be getting less clear, not more. Take a concrete example: let the two points be $(0, 0)$ and $(0, 1)$. What is the "minimal border" if not the line segment $\\{(0, t) \mid 0 \le t \le 1\\}$? (more) |
— | almost 3 years ago |
| Comment | Post #285015 |
Turn the question around: what is *unintuitive* about it? (more) |
— | almost 3 years ago |
| Edit | Post #285016 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285016 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285016 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How can Cross Multiplication be intuited or pictured? average(average(a,b),c) vs. average(a,average(b,c)). 1. The two questions were closed as unclear because they're unclear. There's no dissimulation involved. 2. I don't see any evidence in r's comment that they understood the question. They say that you've ignored suggestions elsewhere for how to improve it, and they reference the introduction, but t... (more) |
— | almost 3 years ago |
| Comment | Post #284996 |
The area of a circle is $\pi r^2$, and a point is the limit of a circle as $r \to 0$. (more) |
— | almost 3 years ago |
| Comment | Post #285005 |
If the question is "Why does dividing two equal things by the same thing give two equal things" then I'm not sure why that isn't intuitive already. Separately, the first image gives a false statement (because you always need to be wary of the special case of division by zero), and I'm not sure what t... (more) |
— | almost 3 years ago |
| Edit | Post #285005 | Question closed | — | almost 3 years ago |
| Comment | Post #284997 |
I can't even guess at what you're asking. (more) |
— | almost 3 years ago |
| Edit | Post #284997 | Question closed | — | almost 3 years ago |
| Edit | Post #284788 | Question closed | — | about 3 years ago |
| Comment | Post #284773 |
@#54114, when r~~ gave essentially the same answer in comments saying that it wasn't clear whether it was what you were looking for, your response was much more lukewarm. (more) |
— | about 3 years ago |
| Edit | Post #284550 |
Post edited: |
— | about 3 years ago |
| Edit | Post #282737 |
Post edited: |
— | about 3 years ago |
| Comment | Post #284550 |
Is "transpose matrix" a technical term from some field (perhaps mathematical physics) or should the tag be changed to `matrix-transpose`? (more) |
— | about 3 years ago |