trace.tensor {tensorA} | 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...i_n j_1...j_n k_1...k_d}
the tensor. Then the result is given by
E_{k_1...k_d}=sum_{i_1...i_n} X_{i_1...i_n i_1...i_n k_1...k_d}
With the Einstein summing convention we would write:
E_{k_1 … k_d}=X_{i_1… i_n j_1… j_n k_1 … k_d}δ_{i_1j_1}… δ_{i_nj_n}{ E_{k_1...k_d}=X_{i_1...i_n j_1...j_n k_1 ... k_d}δ_{i_1j_1} ... δ_{i_nj_n } }
A tensor like X with the i and j dimensions removed.
K. Gerald van den Boogaart
A <- to.tensor(1:20,c(i=2,j=2,k=5)) A trace.tensor(A,"i","j")