trace.tensor | R Documentation |
Collapses the tensor over dimensions i and j. This is like a trace for matrices or like an inner product of the dimensions i and j.
trace.tensor(X,i,j)
X |
the tensor |
i |
a numeric or character vector of dimensions of |
j |
a numeric or character vector of dimensions of |
Let be
X_{i_1\ldots i_n j_1\ldots j_n k_1 \ldots k_d}
the tensor. Then the result is given by
E_{k_1 \ldots k_d}=sum_{i_1\ldots i_n} X_{i_1\ldots i_n
i_1\ldots i_n k_1 \ldots k_d}
With the Einstein summing convention we would write:
E_{k_1 \ldots k_d}=X_{i_1\ldots i_n j_1\ldots j_n k_1 \ldots
k_d}\delta_{i_1j_1}\ldots \delta_{i_nj_n}{
E_{k_1...k_d}=X_{i_1...i_n j_1...j_n k_1 ...
k_d}\delta_{i_1j_1} ... \delta_{i_nj_n
}
}
A tensor like X with the i and j dimensions removed.
K. Gerald van den Boogaart
mul.tensor
, to.tensor
A <- to.tensor(1:20,c(i=2,j=2,k=5))
A
trace.tensor(A,"i","j")
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