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Warning, the name changecoords has been redefined

Warning, the name changecoords has been redefined


               Maple Stuff with Vectors

Here are some Maple examples with vectors.    They illustrate the syntax
of some useful commands for vector operations, etc.   You can make
the commands ``happen'' by hitting  RETURN at the end of any input
line.   Input lines are in  red  on a color monitor, and they start
with a    >  symbol.

To work with vectors, the first step is to load a package of vector things,
called      linalg.     Here's how to load it:


> with( linalg );
The result is to load a whole slew of vector-  and matrix-oriented commands (most
of which we'll have no use for).     Note that among the commands loaded
are      crossprod    and   dotprod.    They do what you'd think.

Let's define some vectors for Maple to work with.  We do so using the vector
command, as follows:


> v := vector( [1,2,3] );
> w := vector( [4,5,6] );
Now let's do some things with these vectors:

> dotprod( v,w );
> dotprod( w,v );
> crossprod( v,w );
> crossprod( w,v );
Does that look right?   


> n := crossprod( v,w );
> crossprod( n, n );
> crossprod( v+w, v-w );
> crossprod( 2*v,3*v);
> 2*v+3*w;
That's all very nice, but what's the numerical answer?

Here's how to get it:

> evalm(");
The   evalm   command    ``evaluates''  a vector or matrix   to
more or less numerical form.


Here's another useful  linear algebra style command.

> m := matrix( [[1,2,3],[2,3,4],[3,4,5]] );
> rref(m);