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I am looking for a program to visualize vector spaces. Ideally this is in the set of real numbers. For instance what shape does the following vertex in $\Bbb R^3$ represent? Vertices are: $\{(1,0,0),(0,2,0),(0,0,0)\}$

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    @utdiscant vector spaces in R3, but if this program can't do points its useless.2012-03-10

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You can use pretty much anything for such a simple task. I give two examples of powerful and free software packages. One is Scilab:

scilab plot

created with

points = [0 0 0; 1 0 0; 0 2 0; 0 0 0]; // repeated endpoint to close the curve param3d(points(:,1),points(:,2),points(:,3));  // creates the plot p=get("hdl"); p.foreground=2; p.thickness=3;  // cosmetics: color and thickness 

The actual plot (but not this illustration) can be rotated with a mouse to better visualize the position of the points in space.

But if you prefer something with simpler syntax, the Sage command

point([(1,0,0),(0,2,0),(0,0,0)]) 

does the job.