proof of inverse of matrix with small-rank adjustment
We will first prove the formula when .
Suppose that is invertible. Thus
Multiply by from the left, and multiply by from the right, we get
The right hand side is equal to , while the left hand side can be factorized as
After rearranging, we obtain
For the general case , consider
We can apply (*) with replaced by .
|Title||proof of inverse of matrix with small-rank adjustment|
|Date of creation||2013-03-22 15:46:08|
|Last modified on||2013-03-22 15:46:08|
|Last modified by||kshum (5987)|