Inverse of A
Suppose where and are orthonormal bases for .
To solve is a three step process.
If is invertible you can write where does all three steps at once.
You can also write as a product where matrix does step .
Step 1: Find coords of . Since is an orthonormal basis the coords are .
Choose . Then .
Step 2: Divide the numbers by the singular values.
Step 3: Use the entries of as the coords of .
Combining all three steps, the solution to is
If is invertible, then the solution to is just . So it's a safe bet that the product is really just .
(Q43) Suppose .
Express as a product of three matrices.
Of course since step 2 divides by the singular values, this procedure only works if the none of the singular values is zero. What happens if ???
Copyright © 2007 Todd Will
Created by Mathematica (April 15, 2007)