Comments on: Matrix identities as derivatives of determinant identities

By: Study Hacks » Blog Archive » You Can Be Busy or Remarkable — But Not Both

Wed, 03 Apr 2013 20:02:47 +0000

[...] new year, he’s written nine long posts, full of mathematical equations and fun titles, like “Matrix identities as derivatives of determinant identities.” His most recent post is 3700 words long! And that’s a normal [...]

By: Supercommutative gaussian integration, and the gaussian unitary ensemble « What’s new

Wed, 20 Feb 2013 04:57:41 +0000

[...] later in this post. By the trick of matrix differentiation of the determinant (as reviewed in this recent blog post), one can also use this method to compute matrix-valued statistics such [...]

By: Craig Tracy

Craig Tracy — Mon, 18 Feb 2013 06:54:42 +0000

For an account of the use of the Sylvester det identity, det(I+AB)=det(I+BA), in random matrix theory, see C. Tracy & H. Widom, “Correlation functions, cluster functions and spacing distributions for random matrices”, J. of Statistical Physics 92 (1998) 809-835.

http://www.math.ucdavis.edu/~tracy/selectedPapers/1990s/CV59.pdf

By: Artificial Intelligence Blog · “Matrix identities as derivatives of determinant identities”

Thu, 14 Feb 2013 14:47:49 +0000

[...] Check out Terence Tao‘s wonderful post ”Matrix identities as derivatives of determinant identities“. [...]

By: I am not an anoymous

I am not an anoymous — Wed, 06 Feb 2013 14:31:28 +0000

I use freegate + Autoproxy(a plugin of firefox) to circumvent the GFW,you can download freegate here:http://forums.internetfreedom.org/index.php?topic=18444.0

Also,there are several other ways to circumvent the great firewall of China,there are some discussion here:

http://terrytao.wordpress.com/2009/04/27/wordpress-blocked-again-by-great-firewall-of-china/

By: Terence Tao

Terence Tao — Wed, 06 Feb 2013 02:47:46 +0000

Oops, I didn’t set up the matrices correctly. It should be OK now…

By: anonymous

anonymous — Tue, 05 Feb 2013 22:39:46 +0000

Dear Professor Tao,

I did the calculation of the products of the two matrices X and Y, and it does not seem to give the Sylvester determinant equaltiy. Could this point be further elaborated on?

By: teobanica

teobanica — Thu, 31 Jan 2013 23:23:29 +0000

Hello, I’m teaching some linear algebra this semester, and, as always, quite hard to get through the first definitions, as to be able to start speaking about the magics of .. There’s actually this problem with the very definition of : is that a volume (intuitive and nice and everything), or some more abstract thing? I learned in Romania, using abstract stuff, now I’m teaching in France, and I have to use abstract stuff as well (otherwise I’d be probably put on the death row by my colleagues :) On the other hand a Russian colleague of mine told me that, at least some 20 years ago, was by definition a volume, in Moscow! (that’s probably why Russians are so good at it) I was wondering how the situation in the US is: any choice allowed? For math students of course.

By: Mark Meckes

Mark Meckes — Thu, 31 Jan 2013 21:01:52 +0000

I’m also delighted to discover that telling my browser to print this page results in a printout of the content of the post without all the links on the left.

By: Amit Bhaya

Amit Bhaya — Thu, 31 Jan 2013 00:26:25 +0000

There’s also the lovely and well known formula \det \exp A = \exp trace(A) with its connection to Liouville’s theorem on conservation of phase space volume by Hamiltonian flows (since Hamiltonian matrices have zero trace).