Theoretical Computer Science Stack Exchange is a question and answer site for theoretical computer scientists and researchers in related fields. Join them; it only takes a minute:

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

Consider the problem:

$\min_X ||XAX^T||_F$

s.t. $X^TX=I$

If A and X are real matrices, the lagrangian will be $tr(XAX^TXA^TX^T)+\sum_i\alpha_i(x_i^Tx_i-1)+\sum_i\sum_{j\neq i}\beta_{ij} q_i^Tq_j$ where $\alpha_i$ and $\beta_{ij}$ are Lagrangian multipliers.

Can I apply $X^TX=I$ here such that the Lagrangian becomes $tr(XAA^TX^T)+\sum_i\alpha_i(x_i^Tx_i-1)+\sum_i\sum_{j\neq i}\beta_{ij} q_i^Tq_j$?

share|cite|improve this question
This question would be more appropriate on math.SE – Suresh Venkat Dec 28 '12 at 6:55

Your Answer


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

Browse other questions tagged or ask your own question.