Two matrices A and B are equal to each other, written A = B, if they have the same dimensions m×n and the same elements a_(i j) = b_(i j) for i = 1, ..., n and j = 1, ..., m. Gradshteyn and Ryzhik call an m×n matrix A "equivalent" to another m×n matrix B iff B = P A Q for P and Q any suitable nonsingular m×m and n×n matrices, respectively.