I want to simplify this term where:
- s is a n x 1 vector
- z and z' are a n x 1 vector
- and D is a n x n matrix
I know that by changing the place of a matrix inside the multiplication will mess up the result. For example, can i multiply by s the whole equation so the 1/s will go away? or use z as a common factor? essentially what rules can i follow in these type of equations that they won't break them?
$$ \frac{1}{s} * z' = \frac{1}{s} * z - \frac{1}{1+ tr(D*\frac{1}{s}*z)}*\frac{1}{s}*z*D*\frac{1}{s}*z $$