7,660 reputation
822
bio website linkedin.com/in/gt6989b
location New York, NY
age 36
visits member for 3 years, 2 months
seen Oct 20 at 1:37

Mar
27
comment Degeneracy number of a ring graph
@triomphe yes, i am now confused too. the definition on wiki does not restrict graph size. need to look more into it, i am sorry.
Mar
27
comment Degeneracy number of a ring graph
@triomphe your last formulation is wrong, degeneracy is $$\min\{\max \mathrm{deg}(s) | s \in S\}.$$ This way, tree is 1-degenerate and cycle is 2-degenerate and star is 1-degenerate also. I got confused myself also, sorry.
Mar
26
comment Mixed integration problem
very nice trick
Mar
26
comment How do I do Linearization at a point that lies on a curve?
@Cozen $a=1$, so when all is done you get a linear function of $x$, hence the name linearization.
Mar
26
comment Double integral of $e^{x^2+y^2}dydx$?
Do you know about polar coordinates? Do you know about the Normal distribution? In what context are you asking this question, for which class is this the homework for?
Mar
26
comment Degeneracy number of a ring graph
@triomphe Yes, exactly.
Mar
26
comment What kind of a mean value is this?
@user3085931 That it is an average means that some actual values could (and likely will) be higher and some could (and likely will) be lower. Average must be in the middle, so it cannot be some will match exactly and others will be all higher or all lower. You should have a mix.
Mar
26
comment What kind of a mean value is this?
@user3085931 I am not familiar with your process's terms, but if I had to explain to someone in English what that quantity was, this is the term I would use.
Mar
26
comment Understanding Integral
Generally, $\int dF(x) = \int F'(x) dx$ which is sometimes written as $\int f(x) dx$ where $f(x) = F'(x)$. But I've never seen $\int dF(x) = \int F(x)dx$.
Mar
26
comment How to show a subset doesn't span a space?
This is an example of something on the span of the first set that is not on the span of the second set. Thus, the second span must be included in the first but the first is larger
Mar
26
comment Find a change in variable that will reduce the quadratic form to a sum of squares
after you are done with arithmetic you end up with $(...)^2 + (***)^2$ so change variables to have $a = ...$ and $b = ***$ and you get $a^2 + b^2$
Mar
26
comment Find a change in variable that will reduce the quadratic form to a sum of squares
Yes, rename $\left(x_1,x_2,x_3\right) \to (x,y,z)$ for convenience, then add and subtract $y^2$ and then factor out the $-$ in front of the $y,z$ terms.
Mar
25
comment Is determinant of matrix multiplied its transpose always positive?
@Pouya just like a square matrix can have complex eigenvalues, the rectangular matrix can have complex singular values, which would make the final result task but negative
Mar
25
comment Is determinant of matrix multiplied its transpose always positive?
@nam Yes, for square matrices this holds. For rectangular, you have to use similar value decomposition
Mar
25
comment Is determinant of matrix multiplied its transpose always positive?
Well, $\det(A)$ is not exactly defined for non-square $A$, and here $A$ is definitely rectangular, you cannot assume $m \neq n$
Mar
25
comment What speed can he drive?
Any thoughts of your own?
Mar
21
comment Is excess kurtosis for a mixture of two normal distributions with the same means and different variances always positive?
@brittUWaterloo I'm sorry, no immediate thoughts on it.
Mar
20
comment Bound for probability of the intersection of a set of events
@EricTowers you supposedly want something converging to $0$ as $N \to \infty$, like OP's product, which results in $p^N$...
Mar
20
comment How many skew symmetric matrices are possible?
@Sabyasachi of course it must be square. But there is still uncountably infinitely many.
Mar
20
comment How many skew symmetric matrices are possible?
@Sabyasachi $A^T = -A$ (as opposed to "just" symmetric, which is $A^T = A$)