In linear algebra, two rectangular m-by-n matrices A and B are called equivalent if B = Q − 1 A P {\displaystyle B=Q^{-1}AP} for some invertible n-by-n matrix P and some invertible m-by-m matrix Q. Equivalent matrices represent the same linear transformation V → W under two different choices of a pair of bases of V and W, with P and Q being the change of basis matrices in V and W respectively. Wikipedia