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NewLinearAlgebraPaclet

Guides

  • Matrices

Symbols

  • AntidiagonallySymmetrizableMatrixQ
  • AntidiagonalMatrix
  • AntidiagonalMatrixQ
  • Antidiagonal
  • AntidiagonalTranspose
  • DesymmetrizedMatrix
  • DeTriangularizableMatrixQ
  • DeTriangularizeMatrix
  • HessianMatrix
  • JacobianMatrix
  • LeftArrowMatrix
  • LowerArrowMatrix
  • LowerRightTriangularize
  • LowerRightTriangularMatrixQ
  • MatrixSymmetrizability
  • PyramidMatrix
  • ReflectedDiagonalMatrix
  • RightArrowMatrix
  • TopArrowMatrix
  • UlamMatrix
  • UpperLeftTriangularize
  • UpperLeftTriangularMatrixQ
PeterBurbery`NewLinearAlgebraPaclet`
HessianMatrix
​
HessianMatrix
[function,ls]
computes the Hessian matrix of second derivatives of
function
with respect to the list of indeterminates/variables
ls
.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Consider the function
f(x,y)=
2
x
+
2
y
. Find the Hessian matrix of this function:
In[1]:=
HessianMatrix
[
2
x
+
2
y
,{x,y}]
Out[1]=
{{2,0},{0,2}}
Consider the function
f(x,y)=
3
x
+
3
y
. Find the Hessian matrix of this function:
In[2]:=
HessianMatrix
[
3
x
+
3
y
,{x,y}]
Out[2]=
{{6x,0},{0,6y}}
Consider the function
f(x,y)=
2
x
y+x
2
y
. Find the Hessian matrix of this function:
In[3]:=
TraditionalForm@
HessianMatrix
[
2
x
y+x
2
y
,{x,y}]
Out[3]//TraditionalForm=
2y
2x+2y
2x+2y
2x
Consider the function
f(x,y)=
x

siny
. Find the Hessian matrix of this function:
In[4]:=
TraditionalForm@
HessianMatrix
[Exp[x]Sin[y],{x,y}]
Out[4]//TraditionalForm=
x

sin(y)
x

cos(y)
x

cos(y)
-
x

sin(y)
Consider the function
f(x,y,z)=
2
x
+
2
y
+
2
z
-2xy-2xz-2yz
. Find the Hessian matrix of this function:
In[5]:=
TraditionalForm@
HessianMatrix
[
2
x
+
2
y
+
2
z
-2xy-2xz-2yz,{x,y,z}]
Out[5]//TraditionalForm=
2
-2
-2
-2
2
-2
-2
-2
2
Consider the function
f(x,y)=
2y
x
+x
2
y
. Find the Hessian matrix of this function:
In[6]:=
TraditionalForm@
HessianMatrix
[
2y
x
+x
2
y
,{x,y}]
Out[6]//TraditionalForm=
2y(2y-1)
2y-2
x
2
2y-1
x
+4y
2y-1
x
log(x)+2y
2
2y-1
x
+4y
2y-1
x
log(x)+2y
4
2y
x
2
log
(x)+2x
This is a symmetric matrix:
In[7]:=
SymmetricMatrixQ
HessianMatrix
[
2y
x
+x
2
y
,{x,y}]
Out[7]=
True
SeeAlso
SymmetricMatrixQ
 
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""

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