Re: Mathematica question about commutativity of multiplication

*To*: mathgroup at smc.vnet.net*Subject*: [mg96727] Re: Mathematica question about commutativity of multiplication*From*: Simon <simonjtyler at gmail.com>*Date*: Mon, 23 Feb 2009 05:00:54 -0500 (EST)*References*: <gnq6u3$89g$1@smc.vnet.net>

Hi James, I think that 1) and 3) are related. Mathematica by default assumes that variables commute (in fact it's hard to change this behaviour) . Your problem probably is that to get a times b, you need to enter a (space) b. With out the space, ab is a variable all by itself and different from ba. As for 2), the eigenvalues are found by solving the secular equation: Det[A-x 1]=0 for the eigenvalues x. This is a n'th order polynomial equation for matrices of size n. Thus you need the roots of high order polynomials. In general these can not be written in closed form, and so mathematica will output Root[] objects. The #1 refers to the variable of the pure function whose root is being found. I think that's enough to get you started... Simon