Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The equation \begin{align} \min_{X}~trace(CX^{T}MX) \end{align} where $C$ is symmetric and M is symmetric , p.s.d can be minimized by defining $M=F^{T}F$ ($M$ being a psd matrix, you will be able to find such a $F$)

and defining $Y=FX$,

we get the above problem as minimizing \begin{align} \min_{Y}~trace(CY^{T}Y) \end{align}

Now if $Y^*$ is the optimal solution would $X^*=YF^{-1}$ be the optimal solution for $X$ for minimizing $trace(CX^{T}MX)$ as we defined $Y$ as $Y=FX$?

share|cite|improve this question
up vote 1 down vote accepted

If $Y=FX$ then multiply on the left by $F^{-1}$ to get $F^{-1}Y=X$, matrix multiplication is not commutative.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.