What is the Commutative Property of Vector Multiplication?

[Butelle]

Homework Statement

I am trying to prove an identity and in order to finish the proof i need to show that:
for z a p-dimensional vector and A a non-singular square (pXp) matrix - also note that T is transpose - :
zTA^(-1)z = zzTA^(-1), where -1 denotes the inverse

I have looked everywhere to find vector multiplication that commutes but so far can't find a rule...


Thanks for your help!

 

[gabbagabbahey]

That doesn't look right to me...$z^TA^{-1}z$ is a scalar (assuming $z$ is a column vector), while $zz^TA^{-1}$ is a $p\times p$ matrix...what was the original problem?

 

[Butelle]

Hey Gabby - thank you for pointing that out (i can't believe i didnt see that!).

I will try it again now - maybe I have done some stupid mistake.