Positivo Definitivo de una funcion en Matlab.pdf
3
() = [ 2 () 1 2 2 () 1 2 2 () 2 1 2 () 2 2 ] () = [ 4 −3 −3 4 ] () 1 = 4 1 − 3 2 2 () 1 2 =4 2 () 1 2 = −3 () 2 = −3 1 + 4 2 2 () 2 2 =4 2 () 2 1 = −3 >> syms x1 x2 f = 2*x1^2-3*x1*x2+2*x2^2 f = 2*x1^2 - 3*x1*x2 + 2*x2^2 >> pretty(f) 2 2 2 x1 - 3 x1 x2 + 2 x2 >> fx1 = diff(f,x1,1)
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Transcript of Positivo Definitivo de una funcion en Matlab.pdf
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() =
[ 2()
12
2()
122()
21
2()
22 ]
() = [
4 33 4
]
()
1= 41 32
2()
12 = 4
2()
12= 3
()
2= 31 + 42
2()
22 = 4
2()
21= 3
>> syms x1 x2
f = 2*x1^2-3*x1*x2+2*x2^2
f =
2*x1^2 - 3*x1*x2 + 2*x2^2
>> pretty(f)
2 2
2 x1 - 3 x1 x2 + 2 x2
>> fx1 = diff(f,x1,1)
-
()
1=
2()
12 =
2()
12=
()
2=
2()
22 =
2()
21=
() =
() =
fx1 =
4*x1 - 3*x2
>> pretty (fx1)
4 x1 - 3 x2
>> fx1x1 = diff(f,x1,2)
fx1x1 =
4
>> fx1x2 = diff(fx1,x2,1)
fx1x2 =
-3
>> fx2 = diff(f,x2,1)
fx2 =
4*x2 - 3*x1
>> pretty (fx2)
4 x2 - 3 x1
>> fx2x2 = diff(f,x2,2)
fx2x2 =
4
>> fx2x1 = diff(fx2,x1,1)
fx2x1 =
-3
>> A=[fx1x1 fx1x2; fx2x1 fx2x2]
A =
[ 4, -3]
[ -3, 4]
>> det(A)
ans =
7
-
() =
() =
>> [A,D]=eig([fx1x1 fx1x2; fx2x1 fx2x2])
A =
[ 1, -1]
[ 1, 1]
D =
[ 1, 0]
[ 0, 7]
