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I have this problem where I have to compute the gradient and justify all the steps. I'm not sure how to start this task of, when calculating for a matrix. Here is the problem: $$\nabla(\mathbf x^T\mathbf x)$$ where $\mathbf x$ is an $n$-vector.

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Let's not work with a matrix directly if it's the bottleneck,

Hint: $$x^Tx = x_1^2 + \ldots +x_n^2$$

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