Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`NewLinearAlgebraPaclet`
HessianMatrix  |
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Details and Options
Examples
(1)
Basic Examples
(1)
Consider the function . Find the Hessian matrix of this function:
f(x,y)=+
2
x
2
y
In[1]:=
 | HessianMatrix |
2
x
2
y
Out[1]=
{{2,0},{0,2}}
Consider the function . Find the Hessian matrix of this function:
f(x,y)=+
3
x
3
y
In[2]:=
| HessianMatrix |
3
x
3
y
Out[2]=
{{6x,0},{0,6y}}
Consider the function . Find the Hessian matrix of this function:
f(x,y)=y+x
2
x
2
y
In[3]:=
TraditionalForm@
[y+x,{x,y}]
 | HessianMatrix |
2
x
2
y
Out[3]//TraditionalForm=
2y | 2x+2y |
2x+2y | 2x |
Consider the function . Find the Hessian matrix of this function:
f(x,y)=siny
x
In[4]:=
TraditionalForm@
[Exp[x]Sin[y],{x,y}]
| HessianMatrix |
Out[4]//TraditionalForm=
x | x |
x | - x |
Consider the function . Find the Hessian matrix of this function:
f(x,y,z)=++-2xy-2xz-2yz
2
x
2
y
2
z
In[5]:=
TraditionalForm@
[++-2xy-2xz-2yz,{x,y,z}]
| HessianMatrix |
2
x
2
y
2
z
Out[5]//TraditionalForm=
2 | -2 | -2 |
-2 | 2 | -2 |
-2 | -2 | 2 |
Consider the function . Find the Hessian matrix of this function:
f(x,y)=+x
2y
x
2
y
In[6]:=
TraditionalForm@
[+x,{x,y}]
| HessianMatrix |
2y
x
2
y
Out[6]//TraditionalForm=
2y(2y-1) 2y-2 x | 2 2y-1 x 2y-1 x |
2 2y-1 x 2y-1 x | 4 2y x 2 log |
This is a symmetric matrix:
In[7]:=
SymmetricMatrixQ
[+x,{x,y}]
| HessianMatrix |
2y
x
2
y
Out[7]=
True
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