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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`
JacobianMatrix
​
JacobianMatrix
[vector,ls]
computes the Jacobian matrix for the vector-valued function represented by the
vector
vector with the indeterminates in the list
ls
.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
In[1]:=
TraditionalForm
JacobianMatrix
[{
2
x
y,5x+Sin[y]},{x,y}]
Out[1]//TraditionalForm=
2xy
2
x
5
cos(y)
In[2]:=
TraditionalFormDet
JacobianMatrix
[{
2
x
y,5x+Sin[y]},{x,y}]
Out[2]//TraditionalForm=
2xycos(y)-5
2
x
In[3]:=
TraditionalFormFullSimplifyDet
JacobianMatrix
[{
2
x
y,5x+Sin[y]},{x,y}]
Out[3]//TraditionalForm=
x(2ycos(y)-5x)
In[4]:=
TraditionalForm
JacobianMatrix
[{rCos[φ],rSin[φ]},{r,φ}]
Out[4]//TraditionalForm=
cos(φ)
-rsin(φ)
sin(φ)
rcos(φ)
In[5]:=
TraditionalFormDet
JacobianMatrix
[{rCos[φ],rSin[φ]},{r,φ}]
Out[5]//TraditionalForm=
r
2
sin
(φ)+r
2
cos
(φ)
In[6]:=
TraditionalFormFullSimplifyDet
JacobianMatrix
[{rCos[φ],rSin[φ]},{r,φ}]
Out[6]//TraditionalForm=
r
In[7]:=
TraditionalForm
JacobianMatrix
[{ρSin[φ]Cos[θ],ρSin[φ]Sin[θ],ρCos[φ]},{ρ,φ,θ}]
Out[7]//TraditionalForm=
cos(θ)sin(φ)
ρcos(θ)cos(φ)
-ρsin(θ)sin(φ)
sin(θ)sin(φ)
ρsin(θ)cos(φ)
ρcos(θ)sin(φ)
cos(φ)
-ρsin(φ)
0
In[8]:=
TraditionalFormDet
JacobianMatrix
[{ρSin[φ]Cos[θ],ρSin[φ]Sin[θ],ρCos[φ]},{ρ,φ,θ}]
Out[8]//TraditionalForm=
2
ρ
2
sin
(θ)
3
sin
(φ)+
2
ρ
2
cos
(θ)
3
sin
(φ)+
2
ρ
2
sin
(θ)sin(φ)
2
cos
(φ)+
2
ρ
2
cos
(θ)sin(φ)
2
cos
(φ)
In[9]:=
TraditionalFormFullSimplifyDet
JacobianMatrix
[{ρSin[φ]Cos[θ],ρSin[φ]Sin[θ],ρCos[φ]},{ρ,φ,θ}]
Out[9]//TraditionalForm=
2
ρ
sin(φ)
In[10]:=
TraditionalForm
JacobianMatrix
[
x
1
,5
x
3
,4
2
x
2
-2
x
3
,
x
3
Sin[
x
1
],{
x
1
,
x
2
,
x
3
}]
Out[10]//TraditionalForm=
1
0
0
0
0
5
0
8
x
2
-2
x
3
cos(
x
1
)
0
sin(
x
1
)
In[11]:=
TraditionalForm
JacobianMatrix
[5
x
2
,4
2
x
1
-2Sin[
x
2
x
3
],
x
2
x
3
,{
x
1
,
x
2
,
x
3
}]
Out[11]//TraditionalForm=
0
5
0
8
x
1
-2
x
3
cos(
x
2
x
3
)
-2
x
2
cos(
x
2
x
3
)
0
x
3
x
2
In[12]:=
TraditionalFormDet
JacobianMatrix
[5
x
2
,4
2
x
1
-2Sin[
x
2
x
3
],
x
2
x
3
,{
x
1
,
x
2
,
x
3
}]
Out[12]//TraditionalForm=
-40
x
1
x
2
SeeAlso
HessianMatrix
RelatedGuides
▪
Matrices
""

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