Re: Eigenvalues, eigenvectors, matrix ranks, determinants, and all that stuff

*To*: mathgroup at smc.vnet.net*Subject*: [mg125507] Re: Eigenvalues, eigenvectors, matrix ranks, determinants, and all that stuff*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Fri, 16 Mar 2012 06:32:17 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 3/15/12 at 12:31 AM, kparchevsky at gmail.com (Konstantin) wrote: <snip> >Very often algebraic manipulations in Mathematica do not produce >expected result just because we and the program have different >defaul assumptions about type of variables. So I tried to specify >EVERYTHING about my variables explicitly ( @ means "belongs to", != >means "not equal" ) >$Assumptions = u@Reals && u!=0 && Bx@Reals && By@Reals && Bz@Reals >&& Bx!=0 && By!=0 && Bz!=0 && rho>0 && cs>0; Unless you have re-defined @ (an ill advised thing to do) you are not repeat not free to use it to do something other than the built-in definition. That is Mathematica interprets u@Reals as the function u with argument Reals, i.e: In[9]:= u@Reals Out[9]= u(\[DoubleStruckCapitalR]) If you want to declare u to be a real variable use the function Element that performs exactly this function That is the statement {u, Bx, By, Bz} \[Element] Reals defines the list of variables all to be real. And note, In[10]:= Reduce[{Element[x, Reals] && x != 0}, x] Out[10]= x<0\[Or]x>0 That is stating x != 0 is sufficient to declare x to be real since the comparison of x to 0 is not valid unless x is real