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

• To: mathgroup at smc.vnet.net
• Subject: [mg125561] Re: Eigenvalues, eigenvectors, matrix ranks, determinants, and all that stuff
• From: Konstantin <kparchevsky at gmail.com>
• Date: Mon, 19 Mar 2012 04:54:49 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```On Mar 16, 4:33 am, Bill Rowe <readn... at sbcglobal.net> wrote:
> On 3/15/12 at 12:31 AM, kparchev... 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:= u@Reals
>
> Out= 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:= Reduce[{Element[x, Reals] && x != 0}, x]
>
> Out= 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

I do not use symbol @ in my code. I use standard symbol "belongs to"
to specify, that u is real. There is no equivalent for this symbol in
ASCII table. And I mentioned in brackets, that in my notation @ means
"belongs to". So, syntax is fine. What can you say about the main
point? Why does Mathematica calculates rank of matrix incorrectly and
how can I calculate my eigenvectors other than do simplifications
"manually"?

```

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