2 is a first type x 'A x such real-valued - the vector function x = [x1, x2 ... xn]
When x is not 0 for a vector, x 'A x> 0 is a positive definite,
When x is not 0 for a vector, x 'A x <0 is negative definite,
When x is not 0 for a vector, x 'A x preferably plus or minus, is uncertain.
For an arbitrary function y = f (x1, x2, x3 ... xn), which for the sake of saddle point or extremum (local or global),
1. obtaining a first derivative function, and to make a first derivative equal to zero, that is:
FX1 = 0
fx2 = 0
...
XNTISNG = 0
Acquiring a plurality of points solution of equations - set points, these points are called saddle point.
= (A1, a2, .... an) wherein 1 is represented by a point, a point is additionally b = (b1, b2, b3..bn) ... and so on,
The f (x) at point b n-do the Taylor expansion using the remainder R 3 represents the first derivative (of course provided that the function can be third-order derivative at point b), if the point b is close enough, then the second derivative than R Xiao Xiang consisting of (the premise is convergent),
D = f (b + b_1) -f (b), b_1 b is similar to a base point adjustment (x0 + delta x), where b, are B_1 n-element vector,
b_1 vector is not equal to 0 (is equal to vector b 0 point) D> 0 means that the function value is increased in the vicinity of f (x) b point, the stagnation point b is the minimum value, additional similar situation 2.
The second derivative with item order on the one hand consisting of f (x) n-Taylor deployed point b, it is the second type, here as constant b, B_1 as variables, the book is x0 + h, y0 + k