We want to find a set of which best fits the equation:

, given the m training examples’ input values are

, which is a matrix.

Notice that It is rather than , since we may have a non-zero intercept term, so we add to every training example.

And the target values are

, which is a vector.

We want to find a set of such that is minimized.

Perform the matrix derivative to :

Set the derivative to zero, hence

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