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Inner

Inner
is a generalization of Dot in which f plays the role of multiplication and g of addition.
  • Inner[f, {{a, b}, {c, d}}, {x, y}, g]{g[f[a, x], f[b, y]], g[f[c, x], f[d, y]]}.
  • Like Dot, Inner effectively contracts the last index of the first tensor with the first index of the second tensor. Applying Inner to a rank r tensor and a rank s tensor gives a rank tensor.
  • Inner contracts index n of the first tensor with the first index of the second tensor.
  • The heads of and must be the same, but need not necessarily be List. »
Compute the "inner f" of two lists, with "plus operation" g:
Compute a generalized inner product of a matrix and a vector:
Use familiar operations:
Compute the "inner f" of two lists, with "plus operation" g:
In[1]:=
Click for copyable input
Out[1]=
 
Compute a generalized inner product of a matrix and a vector:
In[1]:=
Click for copyable input
Out[1]=
 
Use familiar operations:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Generalized inner product of two matrices:
Inner product of a matrix with a vector:
Inner product of a vector with a matrix:
Contract over the first index of the first matrix:
Inner works with heads other than List:
The divergence of a vector field is an inner differentiation:
Inner product of two Boolean matrices:
Applying the functions in a list to corresponding arguments:
This gives the scalar product of two vectors:
This does the same thing:
Combining the products with List gives the same result as MapThread:
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