Perpframes, Aligners and Hangers
Linear Systems, Pseudo-Inverse
Matrix Norm, Rank One
When you look at that action you can see why it's natural to call a diagonal matrix a "stretcher" matrix.
The diagonal matrix stretches in the x direction by a factor of "a" and in the y direction by a factor of "b".
You can verify this by hand using the column way to multiply a matrix times a vector:
sends to .
Butsends to .
Check out the action of each of these stretchers.
But note how the stretcher matrix not only stretches the 2D circle but also embeds the ellipse into 3 dimensional space.
1. Check out the following ellipse.
You can get this ellipse by stretching the unit circle by a factor of 3 in the x direction and a factor of 2 in the y direction.
To get the ellipse shown above I would hit the unit circle with (choose
2. Check out the following ellipsoid
You can get this ellipsoid by stretching the unit sphere by
(a) the matrix
(b) the matrix
(c) the matrix