Matrix Approach to Optimization: Hessian Determinant

This video explains Matrix Approach to Optimization by using Hessian Determinant.
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[@quang.5613]

for 3x3, when it would be saddle point?

[@Joshua74801]

For 3x3, H1 is F11, H2 is the determinant of the matrix but what would H3 be?

[@drbilalmehmood206]

For 3x3 Hessian Determinant matrix,
|H1| = f11
|H2| = 2×2
|H3| = 3×3 = |H|
|H3| is same as the determinant of the original matrix |H|.
Same holds for higher order of determinants, e.g., 4x4, 5x5 etc.

[@yackawaytube]

But why?

[@drbilalmehmood206]

one is the calculus approach and this one is the matrix approach.
its up to the individual which method one wants to use.