8,944 reputation
1646
bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 11 months
seen yesterday

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


Nov
4
revised Can basis vectors have fractions?
added 134 characters in body
Nov
4
answered Can basis vectors have fractions?
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?