Matthew Pressland
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 Nov 5 revised re-writing a mathematical expression edited tags Nov 5 comment re-writing a mathematical expression @EmmaTebbs They also use $f$ again in a second expression on the next page, so its more efficient to define it separately. (It also prevents the formula from $K_{\mathrm{int}}$ from breaking over three lines, which would make it harder to read.) Nov 4 awarded Nice Answer Nov 4 comment Can basis vectors have fractions? @Bill Since my point was that the operation of clearing denominators doesn't make sense in general, it didn't seem worth identifying the most general situation in which it does makes sense. Nov 4 revised $f(x)=x^p-a$ is either ireducible or has a root? added 36 characters in body Nov 4 comment $f(x)=x^p-a$ is either ireducible or has a root? Your first assertion is false; if $k=\mathbb{R}$ or $k=\mathbb{C}$, then $f$ is not irreducible for most values of $p$, by the fundamental theorem of algebra. 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 Funny problem. How to average over periodic numbers Oct 31 reviewed Edit Example of non fractional ideal Oct 31 revised Example of non fractional ideal minor grammar fixes