Timeline for Sarrus determinant rule: references, extensions
Current License: CC BY-SA 2.5
18 events
| when toggle format | what | by | license | comment | |
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| Nov 17, 2013 at 12:45 | answer | added | Robin Whitty | timeline score: 2 | |
| Mar 22, 2010 at 1:15 | vote | accept | Eric Schmutz | ||
| Mar 22, 2010 at 1:14 | vote | accept | Eric Schmutz | ||
| Mar 22, 2010 at 1:14 | |||||
| Mar 22, 2010 at 1:09 | vote | accept | Eric Schmutz | ||
| Mar 22, 2010 at 1:14 | |||||
| Mar 22, 2010 at 1:08 | vote | accept | Eric Schmutz | ||
| Mar 22, 2010 at 1:09 | |||||
| Mar 21, 2010 at 23:45 | history | edited | darij grinberg |
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| Mar 21, 2010 at 23:29 | comment | added | darij grinberg | My quotes are actually from 1923 (the fourth volume of Muir). And I must say I have seen better notations in literature from that time. van der Waerden's Modern Algebra is just 7 years younger! | |
| Mar 21, 2010 at 23:23 | answer | added | Kristal Cantwell | timeline score: 1 | |
| Mar 21, 2010 at 23:21 | comment | added | Mariano Suárez-Álvarez | Muir got his book published in 1905. Notation, language, usage and what not has changed immensely since then in the mathematical science! Your complaints are in the same spirit of those I heard from a student some time ago who very seriously complained that Gauss wrote in latin... | |
| Mar 21, 2010 at 23:19 | comment | added | darij grinberg | Here is a sample: "The Law of Extensible Minors is : If any identical relation be established between a number of the minors of a determinant or between the determinant itself and a number of its minors, the determinants being denoted by means of their principal diagonals, then a new theorem is always obtainable by merely choosing a line of new letters with new suffixes and annexing it to the end of the diagonal of every determinant, including those of order 0, occurring in the identity." Well, this belongs to the half of the results that I actually understood. | |
| Mar 21, 2010 at 23:16 | comment | added | darij grinberg | Muir is indeed amazing, but I wouldn't call it an easy reading. It seems to me that British mathematicians used to work with incredibly bulky and obfuscated notation until the middle of the 20th Century, and Muir could be the best example of this. When have you last seen the word "evanescence" in the meaning of "being equal to zero"? In Muir's book, you will read this more than once. And not only doesn't he distinguish between a matrix and its determinant (denoting both as "determinant"), he actually seems proud of it (as seen from his comments on some papers which do use the word "matrix"). | |
| Mar 21, 2010 at 23:11 | comment | added | Gerry Myerson | And if it's not in Muir, try Dodgson, An Elementary Treatise On Determinants. Dodgson, of course, is better known as Lewis Carroll. | |
| Mar 21, 2010 at 22:57 | comment | added | Mariano Suárez-Álvarez | There is an amazing book on determinants and their history by Thomas Muir. That's the first place I'd look. | |
| Mar 21, 2010 at 22:56 | answer | added | darij grinberg | timeline score: 10 | |
| Mar 21, 2010 at 22:56 | comment | added | Kevin O'Bryant | What's $h$? And "Sarrus' Rule"? | |
| Mar 21, 2010 at 22:47 | comment | added | darij grinberg | I should have denoted $Z_3$ by $C_3$; it's the cyclic group on $3$ elements. Note that $D_4$ is the dihedral group with $8$ (not $4$) elements; I know that there are some conflicting notations here. | |
| Mar 21, 2010 at 22:46 | comment | added | darij grinberg | So the trick is that every permutation $\pi\in S_4$ can be uniquely written as $\sigma\xi$, where $\sigma\in Z_3$ (here, $Z_3$ is seen as a subgroup of $S_4$ acting on the four-element set by cyclically permuting its last three elements) and $\xi\in D_4$ (where $D_4$ is the dihedral group generated by the shift $\left(x\mapsto x+1\mod 4\right)$ and the reflection $\left(x\mapsto -x\mod 4\right)$). The $\xi$ corresponds to the application of the Sarrus rule, and the $\sigma$ corresponds to $1$, $R$ rsp. $R^2$. If I find some generalization of this, I'll post it as an answer. | |
| Mar 21, 2010 at 22:32 | history | asked | Eric Schmutz | CC BY-SA 2.5 |