Timeline for polarization/linearization as in jordan forms
Current License: CC BY-SA 4.0
20 events
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| Jul 18, 2022 at 20:22 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://math.meta.stackexchange.com/a/34713/228959
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 10, 2012 at 22:25 | vote | accept | asllearner | ||
| S Jan 10, 2012 at 22:25 | vote | accept | asllearner | ||
| Jan 10, 2012 at 22:25 | |||||
| Jan 10, 2012 at 0:47 | vote | accept | asllearner | ||
| S Jan 10, 2012 at 22:25 | |||||
| Jan 9, 2012 at 16:11 | vote | accept | asllearner | ||
| Jan 9, 2012 at 16:12 | |||||
| Jan 9, 2012 at 14:07 | answer | added | Vladimir Dotsenko | timeline score: 2 | |
| Jan 9, 2012 at 13:27 | answer | added | Tom De Medts | timeline score: 2 | |
| Jan 9, 2012 at 7:09 | comment | added | asllearner | sorry again. without too fine a point: Yes, question is not exclusively related to J.A. but I couldn't find a better tag for it. I know "polar forms" are not so necessary in understanding JA, but JA led to it, which I am interested in in its own right and for its connections to J.A. and other areas (e.g. algebraic geometry, invariant theory (e.g. Weyl), representation theory). My link to castelau/polar forms/blossoms is that it is the only one that I have been able to find documentation about. I am perhaps seeking a basic exposition of "polar forms" less intermingled with other objectives?? | |
| Jan 9, 2012 at 6:35 | comment | added | asllearner | should be: McCrimmon | |
| Jan 9, 2012 at 6:33 | comment | added | asllearner | thanks for helping me.. nevertheless, sorry, I see I really explained myself poorly since i was trying to be brief. my immediate goal is to understand MacCrinnon and how symmetrization works. It is AN eventual goal to also compare it with "polar forms" as explained in Ramshaw (where he relates it to Castelau though this is not primary interest). I think is related because "it is often helpful to study the polar form of F...the unique symmetric, multiaffine function f(u1,...un) satisfying the identity F(t)=f(t,...,t). " For example: $$ t^3+3t^2-6t-8 -> uvw + uv + uw + vw - (u+v+w) -8 $$ | |
| Jan 9, 2012 at 4:45 | comment | added | Will Jagy | Evidently you are way off base, see en.wikipedia.org/wiki/B%C3%A9zier_curve and en.wikipedia.org/wiki/NURBS and en.wikipedia.org/wiki/De_Casteljau%27s_algorithm You really have no need for Jordan algebras. | |
| Jan 9, 2012 at 3:52 | comment | added | Will Jagy | Why De Casteljau's algorithm ? | |
| Jan 9, 2012 at 0:50 | comment | added | asllearner | this link talks about "the classical mathematical principle of the polar form" that may be what I want, but I have never heard of it, cant find anything about it, and though it describes it in some detail, it I would like to see a more transparent exposition: hpl.hp.com/techreports/Compaq-DEC/SRC-RR-34.pdf | |
| Jan 9, 2012 at 0:37 | comment | added | asllearner | eventual goal is to figure out relationship if any to De Casteljau's algorithm | |
| Jan 9, 2012 at 0:33 | comment | added | asllearner | 2. I really have had a hard time finding any links/references about "linearization" (too close to linearizing a function... polarizing (too close to polarized light, etc) symmetrizing (to many other meanings) so I am trying to find out what theory he is talking about and where it was developed...is it a branch of abstract algebra, what? I can understand what a quadratic mapping of a complex space is, but don't know where "linearizing" fits in it??? I don'T mind trying to figure things out myself, but I think I need to be pointed in a direction...or at least confirmed in my thinking. | |
| Jan 9, 2012 at 0:33 | comment | added | asllearner | I guess the core of my questions is two things: he says > take p(x+ λy) for an indeterminate scalar λ and expand this out as > a polynomial in λ: p(x + λy) = p(x) + λp1(x;y) + λ2p2(x;y) + ··· + > λnp(y). in a case like f(x,y,z) = 3x^2yz + 2y^2x^2 + z^2x + z^3y does he mean define p(x)=f(x|y,z) compute p(x+λx')=f2(x,x',y,z) then define p2(y)=f2() compute p2(y+λy')=f3(x,x',y,y',z) define p2(y)=f3() compute p2(z+λz')=f3(x,x',y,y',z,z') | |
| Jan 9, 2012 at 0:18 | comment | added | asllearner | you mean mathematically? A bit hard...education so far in math and physics at the undergraduate level, but from there a smattering of knowledge from many areas, e.g. mathematical physics, e.g. hilbert spaces, quantum theory, linear and abstract algebra, real and complex analysis, basic and advanced calculus, topology and topological spaces, differential geometry, a bit of number theory, even a bit of knot theory...but still just piecing it all together...more broad than deep. I can recognize most mathematical concepts, but not always full up on the details. | |
| Jan 8, 2012 at 22:43 | comment | added | Will Jagy | Tell us something about your background. | |
| Jan 8, 2012 at 21:26 | history | asked | asllearner | CC BY-SA 3.0 |