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I have the following problem:For $\theta \in \mathbb{C}^{n\times1}$, $\quad$ $Y=X\theta+W$

where $W \in \mathbb{C}^{m\times1}$ is the complex additive white Gaussian noise. $X \in \mathbb{C}^{m\times n},Y \in \mathbb{C}^{m\times 1}$ are known. I'd like to solve the following problem:

$\qquad$ $\mathop{\arg\min}_{\theta} \ \ \mathrm{J} (\theta) = \|Y-X\theta\|^2$

$\qquad$ subject to: $\ \ \theta^TA\theta = 0$

where $A \in \mathbb{R}^{n\times n}$ is known, $T$ denote the transpose. Can I solve this problem by Lagrange multipliers and how to do this? And how to get a close-form solution like Least Square with linear equality constraints?

Thanks

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