# Matt Pressland

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bio website people.bath.ac.uk/mdp33 location Bath, United Kingdom age 25 member for 2 years, 10 months seen 2 days ago profile views 924

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

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 Nov4 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. Nov4 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). Nov4 answered What if not connectedness defines a graph? Nov4 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 $\mathbf{u}$. Nov3 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. Nov3 comment Eigenvectors of a Rotation Matrix The assumption of the first question is false; any eigenvector of any matrix can be rescaled arbitrarily. Nov3 revised A leveling on a non-empty set $A$ is a function $d$ from $A \times A$ into $A$… added 108 characters in body Oct31 revised Show that the unit sphere with centre $0$ in $\mathbb{R}^d$ is compact. added 31 characters in body Oct31 reviewed Leave Open Negative index coefficients of Laurent series for 1/sin(z) Oct31 reviewed Leave Open Lubrication Theory: Quick Question! Oct31 reviewed Leave Open Funny problem. How to average over periodic numbers Oct31 reviewed Close How to write $\frac{-2+i }{(1+i)^2}$ in standard form Oct31 reviewed Edit Example of non fractional ideal Oct31 revised Example of non fractional ideal minor grammar fixes Oct31 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 Oct30 answered Question about composition of categories Oct29 revised Homomorphism well defined edited title Oct29 reviewed Edit How to find out the linear transformation? Oct29 revised How to find out the linear transformation? added latex Oct29 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.