Coherent algebra

A coherent algebra is an algebra of complex square matrices that is closed under ordinary matrix multiplication, Schur product, transposition, and contains both the identity matrix

and the all-ones matrix

[1] A subspace

{\displaystyle \mathrm {Mat} _{n\times n}(\mathbb {C} )}

is said to be a coherent algebra of order

if: A coherent algebra

is said to be: The set

of Schur-primitive matrices in a coherent algebra

is defined as

Dually, the set

of primitive matrices in a coherent algebra

is defined as