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

Under what condition(s) a unique solution is available for this over-determined system of equations?

$$ x^TA_1x = x^TA_2x = \cdots = x^TA_{N-1}x $$

where $$ A_d = [w^{d(p_i-p_j)}]_{K \times K} \quad, \qquad w = e^{-j \frac{2\pi}N},\quad \{p_1,p_2,\dots,p_K\} \subseteq \{1,2,\dots,N\} , \quad x \in\mathbb{R}_+^K $$

Obviously for this system to be over-determined $ N - 2 > K $ holds.

Also, how to find the least square solution of this quadratic over-determined system of equations?

share|cite|improve this question

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.