A square matrix 
is skew-symmetrizable if there is a diagonal
matrix 
with positive diagonal entries such that 
is an antisymmetric matrix,
or equivalently
 |
If 
has diagonal entries 
, ..., 
, this condition is
 |
for all 
and 
.
Every antisymmetric matrix is skew-symmetrizable by taking 
to be the identity matrix, but the converse need not hold.
Skew-symmetrizable integer matrices govern seed mutations
in cluster algebras.
