Timeline for polarization/linearization as in jordan forms
Current License: CC BY-SA 3.0
9 events
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| May 27, 2023 at 11:09 | comment | added | The Amplitwist |
The tinyurl link in a comment above points to a Google Books search for "Aronhold polarisation" in the mentioned book by Procesi (Zbl 1154.22001). (Leaving this comment because URL shorteners can easily break, so they should be avoided whenever possible.)
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| Jan 10, 2012 at 22:25 | vote | accept | asllearner | ||
| Jan 10, 2012 at 0:47 | comment | added | asllearner | I see. wow. Thanks. grand hat tip. Sorry to be so peevish....just what I needed. I will check out procesi... | |
| Jan 10, 2012 at 0:47 | vote | accept | asllearner | ||
| Jan 10, 2012 at 22:25 | |||||
| Jan 9, 2012 at 17:48 | comment | added | Vladimir Dotsenko | I actually overlooked that you complained about the available links and asked for textbooks. A reference I like is Procesi, "Lie groups: an approach through invariants and representations", section on Aronhold method. (It is available on Google Books, tinyurl.com/aronhold - check it out.) | |
| Jan 9, 2012 at 17:33 | comment | added | Vladimir Dotsenko | 2. A $4$-dimensional vector space $V$ over real numbers is isomorphic to $\mathbb{R}^4$. If, incidentally, the vector space $V$ is an algebra, you can take the algebra structure with you via an isomorphism of your choice, right? ;-) | |
| Jan 9, 2012 at 17:30 | comment | added | Vladimir Dotsenko | 1. In various contexts related to identities in the noncommutative/nonassociative settings this is quite standard. Check, e.g. the MO question mathoverflow.net/questions/61884/… and the Wikipedia article en.wikipedia.org/wiki/Homogeneous_function#Polarization - to name just two of zillions. | |
| Jan 9, 2012 at 16:42 | comment | added | asllearner | thank you. I get your general point. I have never seen this discussed in any textbook I have read, so I am wondering where it comes from. This is probably a really stupid question...if $x$ is a matrix with entries in $\mathbb{R}$ is it an element of $\mathbb{R}^4$? isn't an element of $\mathbb{R}^4$ a vector (e.g. four-vector with real entries)--yes technically a matrix, but you cant take powers of it...or can you!? | |
| Jan 9, 2012 at 14:07 | history | answered | Vladimir Dotsenko | CC BY-SA 3.0 |