In Textures, I cannot find an explanation of what the X,Y,Z matrix (on the lower left) in the Map Input Tab means. I"ve seen an example or two but no explanation why a certain setting was used.
Will someone point me to a reference for this or provide an explanation of how that matrix is used?
Hi,
the wiki is indeed a bit short on this:
XYZ (x3) - Axes
Re-orders the X, Y and Z coordinates. You can flip axes to mirror a texture, or ignore axes all together.
It’s an Input-Output matrix to map texture space onto object space. Most procedurals deliver 3-dimensional output that resides in texture space. The XYZ-matrix transforms this into object space where the rows are for the input side and the columns for output. The default choice with the buttons in the diagonal activated shows: X mapped to X, Y to Y, Z to Z, no surprises here. The blank spaces at the beginning of each row mean you can disable a texture dimension altogether.
To play around with this, it’s quite illustrative to put a wood texture (with rings) on a cube, enable render preview (Shift-P) and switch around all axis’. E.g.: The default wood texture will show rings on all faces of the cube. If you make a mental image of how the texture extends into 3-dimensional space, it’s like a sphere within a sphere… Disabling one of the texture axis (set to blank) will change it into a tree trunk, looking like a tube within a tube.
Good luck experimenting!
Regards
From top to bottom they are X, Y and Z and by default they are set like that. you can (let’s say) map all of them to X, or all of them to nothing if you use all three boxes on the left or any other combination.
%<
Here is a little bit of an explanation in the wiki:
http://wiki.blender.org/index.php/BSoD/Introduction_to_Materials/part1di
And further towards the end, where you play with the label, moving it with the xyz. If you get stuck come back here and read this:
http://blenderartists.org/forum/showthread.php?t=92769
It can be fun with a few clues! 
All,
Thanks for the help. After experimenting with x,y,and z; it seems a little clearer.
Sincerely,
3DUser