8,899 reputation
1646
bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 10 months
seen 2 days ago

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.


Nov
4
comment Can basis vectors have fractions?
I don't think you said what you mean - if $v$ is a vector in some basis, then $cv$ is definitely not in the basis unless $c=1$! But you can replace $v$ by $cv$ and you will have another basis for the same space.
Nov
4
comment Towers of Hanoi Starting From Initial (Legal) Configuration?
Your description should be close enough though, and I think makes the point clearly - the algorithm will move you from one corner of the triangle to another in a straight line, but your picture explicitly shows the $6$ (at least once you label the pegs) legal configurations that don't occur as a stage in the traditional recursive solution. (And if you increase the number of disks, more such arrangements exist).
Nov
4
answered What if not connectedness defines a graph?
Nov
4
comment Show that the map $T_U:W\to U^{*}$ is linear
$\tau$ isn't the dot product - its arguments even come from two different spaces! It is just some bilinear map $W\times V\to\mathbb{K}$. It's not unusual to use the $U^\perp$ notation for orthogonality with respect to other bilinear forms than the dot product. Since you are given that $\tau$ is bilinear, the question is merely asking you to see that this implies the linearity of $T_U$ - this seems to me to be mainly an exercise in distinguishing linearity of $(T_U\mathbf{w})(\mathbf{u})$ in $\mathbf{w}$ from linearity in $\mathbf{u}$.
Nov
3
comment Eigenvectors of a Rotation Matrix
Even banning the identity matrix isn't enough; the matrix $$\begin{pmatrix}-1&0&0\\0&-1&0\\0&0&1\end{pmatrix}$$ is also a rotation matrix admitting non-orthogonal eigenvectors.
Nov
3
comment Eigenvectors of a Rotation Matrix
The assumption of the first question is false; any eigenvector of any matrix can be rescaled arbitrarily.
Nov
3
revised A leveling on a non-empty set $A$ is a function $d$ from $A \times A$ into $A$…
added 108 characters in body
Oct
31
revised Show that the unit sphere with centre $0$ in $\mathbb{R}^d$ is compact.
added 31 characters in body
Oct
31
reviewed Leave Open Negative index coefficients of Laurent series for 1/sin(z)
Oct
31
reviewed Leave Open Lubrication Theory: Quick Question!
Oct
31
reviewed Leave Open Funny problem. How to average over periodic numbers
Oct
31
reviewed Close How to write $\frac{-2+i }{(1+i)^2}$ in standard form
Oct
31
reviewed Edit Example of non fractional ideal
Oct
31
revised Example of non fractional ideal
minor grammar fixes
Oct
31
revised If some vectors in $\mathbb Q^n$ are linearly independent over $\mathbb Q$ , then are they also linearly independent over $\mathbb C$?
added 6 characters in body; edited title
Oct
30
answered Question about composition of categories
Oct
29
revised Homomorphism well defined
edited title
Oct
29
reviewed Edit How to find out the linear transformation?
Oct
29
revised How to find out the linear transformation?
added latex
Oct
29
comment Homomorphism well defined
The definition of $\theta$ as written appears to depend on whether you write $[a]_n$, or $[a+n]_n$ or $[a-42n]_n$, all of which are equal as sets - you are being asked to show that in fact you get the same answer independent of how you write the set.