A linear combination of Killing tensors is a Killing tensor. A symmetric product of Killing tensors is also a Killing tensor; that is, if  and  are Killing tensors, then  is a Killing tensor too.
A linear assembly of Killing tensors is a Killing tensor. A symmetric multiplication of Killing tensors remains a Killing tensor; that is, if  and  are Killing tensors, then  is also a Killing tensor too.