2. Exact tensor decompositions
You'd think that the usual matrix decompositions could easily be extended to tensors, but this is not the case. In fact, there are major differences as soon as we go from order 2 to order 3, which both make the use of tensors interesting and raise new theoretical and algorithmic difficulties.
2.1 2.1 Tensor rank, polyadic canonical decomposition (CP)
In Example 3, we saw a simple form of tensor, which is very useful in applications, as it represents functions with separate variables. Decomposing a tensor into a sum of simple tensors leads to the first proposition:
Proposition 4: CP decomposition (CPD). Any tensor
Exclusive to subscribers. 97% yet to be discovered!
Already subscribed? Log in!
Exact tensor decompositions
Approximate tensor decompositions
Bibliographical sources
Exclusive to subscribers. 97% yet to be discovered!
Already subscribed? Log in!
Article included in this offer
"Mathematics"
(
168 articles
)
Updated and enriched with articles validated by our scientific committees
A set of exclusive tools to complement the resources
