# leslie townes

(my about me is currently blank)

 Nov 17 answered Linear and Commutative function over Square Matrices. Oct 31 answered Limit of f(x) as x goes to a Oct 30 comment Definition of a logarithmIt's quite possible to "define the logarithm" for negative arguments in an elementary way. But problems arise if you want your new thing have properties on its new domain like the ones the good old logarithm has on its good old domain (e.g.: try to identify the \$x\$ and \$y\$ for which your extended logarithm satisfies \$\log_b(xy) = \log_b(x) + \log_b(y)\$). It's because of these obstacles that I put quotes around "define the logarithm": if what you get fails to resemble the old logarithm in key ways, maybe it's better not to think of the new thing as "the logarithm" without qualification. Oct 24 answered Describe what concavity means in terms if the location of the tangent relative to the function? Oct 24 answered Upper triangular matrix representation for a linear operator Oct 23 awarded Yearling Oct 23 awarded Yearling Jul 30 awarded Nice Question Jun 19 awarded Nice Answer May 7 awarded Necromancer May 7 awarded Good Answer Apr 25 awarded Necromancer Mar 29 awarded Nice Answer Dec 25 awarded Good Answer Dec 22 asked Constructions of the smallest nonabelian group of odd order Nov 15 awarded Necromancer Oct 23 awarded Yearling Oct 23 awarded Yearling Oct 1 comment Boundary between all convergent series on one side and divergent series on the other sideI have never liked this kind of phrasing in textbooks (exercises of this sort are common in analysis books). In my view, it is more appropriate to say that these theorems show that one way (or perhaps even a class of ways) of attempting to formalize a "boundary" between convergent and divergent series will not work. (The fact that one could likely come up with examples dooming any way of trying to do this is interesting, but almost "meta-mathematical," and not really the point.) Someone will surely give more detail about the relevance of this example to a "boundary" in an answer. Aug 14 comment Is there a great book on eigenvalues?A study of abstract linear algebra (ie, vector spaces and linear operators, not matrices and \$\mathbb{R}^n\$) might provide the closest thing to an answer to this question. It can sometimes seem like the "eigenvalues" people mention in varied contexts are different from abstract linear algebra eigenvalues (e.g. because no linear operator or vector space is mentioned, just a physical system, or a differential equation). But with effort it is often possible to identify an operator, specific to each applied context, whose linear algebra eigenvalues are the "eigenvalues" under discussion.