Iterated matrix multiplication is the polynomial obtained by taking a specified entry of a product of matrices whose
entries are distinct commuting variables. For 
matrices 
, ..., 
of size 
,
write
 |
It is homogeneous of total degree 
, in 
ambient variables, including
entries absent from the polynomial. For 
, it is 
. Matrix multiplication gives polynomial-size
arithmetic circuits without a depth restriction.
