Let K {\displaystyle {}K} denote a field, and let I {\displaystyle {}I} and J {\displaystyle {}J} denote index sets. An I × J {\displaystyle {}I\times J} -matrix is a mapping
If I = { 1 , … , m } {\displaystyle {}I=\{1,\ldots ,m\}} and J = { 1 , … , n } {\displaystyle {}J=\{1,\ldots ,n\}} , then we talk about an m × n {\displaystyle {}m\times n} -matrix. In this case, the matrix is usually written as
denote a
field,
and let
and 
denote index sets. An 
-matrix is a
mapping
and
,
then we talk about an 
-matrix. In this case, the matrix is usually written as
