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00:00-03:19 Problem setup. (1/10)
03:19-04:47 Changing notation to make similarity to one variable case. (2/10)
04:47-08:20 Rewriting the formula in coordinate-wise form. (3/10)
08:20-10:43 Critical point and a linear vector field determined by a matrix of second derivatives. (4/10)
10:43-11:25 GLS-decomposition. S=0 (5/10)
11:25-12:59 Case 1.1: L=0 G>0 (6/10)
12:59-13:43 Case 1.2: L=0 G