Conformable matrix

In mathematics, a matrix is conformable if its dimensions are suitable for defining some operation (e.g. addition, multiplication, etc.).

Examples

• In order to be conformable to addition or subtraction, matrices need to have the same dimensions. Thus A, B and C all must have dimensions m × n in the equation
$A + B = C$
or
$A - B = C$
for some fixed m and n.
$AB = C.$
If A has dimensions m × n, then B has to have dimensions n × p for some p, so that C will have dimensions m × p. That is, the number of columns in A must equal the number of rows in B for A and B to be conformable for multiplication in that sequence.
• Since squaring a matrix involves multiplying it by itself ($A^2=AA$) a matrix must be m×m (that is, it must be a square matrix) to be conformable for squaring. Thus for example only a square matrix can be idempotent.