A tensor with entry 1 if and only if three indices are equal

The tensor mapping a tensor of dimension d to its corresponding diagonal tensor of dimension c(d',d*)

tripledelta.tensor(d,mark1="'",mark2="*",dn=NULL)

Arguments

d

the first of three dimension vectors

mark1

the mark for the second dimension vectors

mark2

the mark for the third dimension vectors

dn

list of character vectors, optional dimnames

Value

The tensor given by: $$E_{i_1\ldots i_n j_1\ldots j_n k_1\ldots k_n}=\delta_{i_1j_1}\delta_{i_1k_1} \ldots \delta_{i_nj_n}\delta_{i_nk_1}$$

Details

The tripledelta is the tensor mapping a tensor to a corresponding diagonal tensor.

See also

delta.tensor, diag.tensor

Author

K. Gerald van den Boogaart

Examples

tripledelta.tensor(3)
#> , , 1
#> 
#>       '
#>        [,1] [,2] [,3]
#>   [1,]    1    0    0
#>   [2,]    0    0    0
#>   [3,]    0    0    0
#> 
#> , , 2
#> 
#>       '
#>        [,1] [,2] [,3]
#>   [1,]    0    0    0
#>   [2,]    0    1    0
#>   [3,]    0    0    0
#> 
#> , , 3
#> 
#>       '
#>        [,1] [,2] [,3]
#>   [1,]    0    0    0
#>   [2,]    0    0    0
#>   [3,]    0    0    1
#> 
#> attr(,"class")
#> [1] "tensor"