A tensor can be seen as a linear mapping of a tensor to a tensor. This
function computes the singular value decomposition of this mapping
Usage
svd.tensor(X,i,j=NULL,...,name="lambda",by=NULL)
Arguments
X
The tensor to be decomposed
i
The image dimensions of the linear mapping
j
The coimage dimensions of the linear mapping
name
The name of the eigenspace dimension. This is the
dimension created by the decompositions, in which the eigenvectors
are e_i
...
further arguments for generic use
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.
svd.tensorComputes a singular value decomposition
u_{i_1...i_dλ{}},d_λ{}, v_{j_1...j_l}λ{} such
that u and v correspond to orthogonal mappings from R_λ{} to
R_i or R_j respectively.
Value
a tensor or in case of svd a list u,d,v, of tensors like in svd.