Comments for Felix' Math Place http://math.fontein.de Focussed on, but not limited to Computational Number Theory Mon, 19 Sep 2011 18:10:41 +0000 hourly 1 http://wordpress.org/?v=3.1 Comment on Multiplicity of the Determinant. by Felix Fontein http://math.fontein.de/2010/11/10/multiplicity-of-the-determinant/comment-page-1/#comment-314 Felix Fontein Mon, 19 Sep 2011 18:10:41 +0000 http://math.fontein.de/?p=790#comment-314 And again I regret that I didn't start studying in Oldenburg two years earlier... :) And again I regret that I didn’t start studying in Oldenburg two years earlier… :)

]]> Comment on Multiplicity of the Determinant. by Jens http://math.fontein.de/2010/11/10/multiplicity-of-the-determinant/comment-page-1/#comment-313 Jens Mon, 19 Sep 2011 17:39:47 +0000 http://math.fontein.de/?p=790#comment-313 Hi! This proof looked too familiar to me... and indeed: Quebbemann (WS 99/00) used the same proof in his Lineare Algebra. :) Hi! This proof looked too familiar to me… and indeed: Quebbemann (WS 99/00) used the same proof in his Lineare Algebra. :)

]]> Comment on On a Certain Determinant. by Felix Fontein http://math.fontein.de/2011/03/25/on-a-certain-determinant/comment-page-1/#comment-286 Felix Fontein Mon, 20 Jun 2011 07:49:46 +0000 https://math.fontein.de/?p=814#comment-286 I just noticed that this determinant fits into a more general scheme: the matrix can be written as the sum of $D = diag(x_1, \dots, x_n)$ and $u v^T$, where $u = v$ is the vector with all coefficients being 1. According to <a href="http://planetmath.org/encyclopedia/DeterminantsOfSomeMatricesOfSpecialForm.html" rel="nofollow">planetmath.org</a>, we have $\det(D + u v^T) = \det D + v^T D^\# u$ for arbitrary $D \in K^{n \times n}$, $u, v \in K^n$, where $D^\#$ is the <a href="http://en.wikipedia.org/wiki/Adjugate_matrix" rel="nofollow">adjugate</a> of $D$. For a diagonal $D$, $D^\#$ is a diagonal matrix with the $i$-th diagonal entry being $\prod_{j \neq i} x_j$, whence one obtains the result I've shown above. I just noticed that this determinant fits into a more general scheme: the matrix can be written as the sum of D = diag(x_1, \dots, x_n) and u v^T, where u = v is the vector with all coefficients being 1. According to planetmath.org, we have \det(D + u v^T) = \det D + v^T D^\# u for arbitrary D \in K^{n \times n}, u, v \in K^n, where D^\# is the adjugate of D.
For a diagonal D, D^\# is a diagonal matrix with the i-th diagonal entry being \prod_{j \neq i} x_j, whence one obtains the result I’ve shown above.

]]> Comment on On a Certain Determinant. by Lin http://math.fontein.de/2011/03/25/on-a-certain-determinant/comment-page-1/#comment-285 Lin Sat, 18 Jun 2011 00:41:00 +0000 https://math.fontein.de/?p=814#comment-285 I remembered I saw this determinant before, in my linear algebra course. You may also check with D. Bernstein's . However, the appearace of this determiant you expained seems new to me I remembered I saw this determinant before, in my linear algebra course. You may also check with D. Bernstein’s . However, the appearace of this determiant you expained seems new to me

]]> Comment on How to Compute the 5-adic Expansion of 1/2; or: Hensel’s Lemma and (Non-Analytic) Newton Iteration. by Felix Fontein http://math.fontein.de/2010/02/06/how-to-compute-the-5-adic-expansion-of-12-or-hensels-lemma-and-non-analytic-newton-iteration/comment-page-1/#comment-188 Felix Fontein Sun, 17 Apr 2011 22:22:10 +0000 http://math.fontein.de/?p=690#comment-188 Thanks alot for pointing that out! I just fixed it... Thanks alot for pointing that out! I just fixed it…

]]> Comment on How to Compute the 5-adic Expansion of 1/2; or: Hensel’s Lemma and (Non-Analytic) Newton Iteration. by m0shbear http://math.fontein.de/2010/02/06/how-to-compute-the-5-adic-expansion-of-12-or-hensels-lemma-and-non-analytic-newton-iteration/comment-page-1/#comment-187 m0shbear Sat, 16 Apr 2011 15:41:37 +0000 http://math.fontein.de/?p=690#comment-187 Typesetting error for a_10: you did sum^1 05^n, while what you intended was sum^{10} 5^n Typesetting error for a_10: you did sum^1 05^n, while what you intended was sum^{10} 5^n

]]> Comment on Inequalities. by John Doe http://math.fontein.de/2010/02/09/inequalities/comment-page-1/#comment-171 John Doe Sun, 19 Dec 2010 18:59:07 +0000 http://math.fontein.de/?p=732#comment-171 I understand—anyhow, thanks for your rapid response! I understand—anyhow, thanks for your rapid response!

]]> Comment on Inequalities. by Felix Fontein http://math.fontein.de/2010/02/09/inequalities/comment-page-1/#comment-170 Felix Fontein Sun, 19 Dec 2010 03:54:56 +0000 http://math.fontein.de/?p=732#comment-170 I'd happily provide the .dot file, but unfortunately I cannot find the source files anymore... If I happen to find them again, I'll put them online. I’d happily provide the .dot file, but unfortunately I cannot find the source files anymore… If I happen to find them again, I’ll put them online.

]]> Comment on Inequalities. by John Doe http://math.fontein.de/2010/02/09/inequalities/comment-page-1/#comment-167 John Doe Fri, 17 Dec 2010 15:26:44 +0000 http://math.fontein.de/?p=732#comment-167 Nice idea! But instead of providing a higher resolution bitmap version, you should publish the .dot source file instead. With it, everyone can create a even bigger one – one other formats like .svg. Nice idea!

But instead of providing a higher resolution bitmap version, you should publish the .dot source file instead. With it, everyone can create a even bigger one – one other formats like .svg.

]]> Comment on Rigorous Arithmetic in the Arakelov Divisor Class Group of a Number Field. by spielwiese. » blog archive » nancy. http://math.fontein.de/2010/07/27/rigorous-arithmetic-in-the-arakelov-divisor-class-group-of-a-number-field/comment-page-1/#comment-117 spielwiese. » blog archive » nancy. Tue, 27 Jul 2010 09:58:50 +0000 http://math.fontein.de/?p=778#comment-117 [...] which was held in nancy this time (two years ago, it was in banff). this year i also presented a poster. here are some impressions from the [...] [...] which was held in nancy this time (two years ago, it was in banff). this year i also presented a poster. here are some impressions from the [...]

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