# powertensor: Compute the power of a symmetric tensor In tensorA: Advanced Tensor Arithmetic with Named Indices

## Description

A tensor can be seen as a linear mapping of a tensor to a tensor. If domain and image are the same and the tensor is definite, we can define powers.

## Usage

 `1` ```power.tensor(X,i,j,p=0.5,by=NULL) ```

## Arguments

 `X` The tensor to be decomposed `i` The image dimensions of the linear mapping `j` The domain dimensions of the linear mapping `p` the power of the tensor to be computed `by` the operation is done in parallel for these dimensions

## Details

A tensor can be seen as a linear mapping of a tensor to a tensor. Let denote R_i the space of real tensors with dimensions i_1...i_d.
To compute a power `dim(X)[i]` and `dim(X)[j]` need to be equal and the tensor symmetric between these dimension. Some exponents are only valid with positive definite mappings. None of these conditions is checked.

a tensor

## Note

symmetry of the matrix is assumed but not checked.

## Author(s)

K. Gerald van den Boogaart

`svd.tensor`,
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```A <- to.tensor(rnorm(120),c(a=2,b=2,c=5,d=3,e=2)) AAt <- A %e% mark(A,"'",c("a","b")) AAt power.tensor(AAt,c("a","b"),c("a'","b'"),-1) inv.tensor(AAt,c("a","b")) power.tensor(AAt,c("a","b"),c("a'","b'"),2) mul.tensor(AAt,c("a","b"),AAt,c("a'","b'")) power.tensor(power.tensor(AAt,c("a","b"),c("a'","b'"),1/pi), c("a","b"),c("a'","b'"),pi) AAt <- einstein.tensor(A , mark(A,"'",c("a","b")),by="e") power.tensor(AAt,c("a","b"),c("a'","b'"),-1,by="e") inv.tensor(AAt,c("a","b"),by="e") power.tensor(AAt,c("a","b"),c("a'","b'"),2,by="e") mul.tensor(AAt,c("a","b"),AAt,c("a'","b'"),by="e") power.tensor(power.tensor(AAt,c("a","b"),c("a'","b'"),1/pi,by="e"), c("a","b"),c("a'","b'"),pi,by="e") ```