transformation matrix

noun1

1. •
   A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ.

   • Given a linear transformation T(x) in functional form, its transformation matrix can be constructed by applying T to each vector of the standard basis, then inserting the results into the columns of the new matrix.
   • A transformation matrix of dimension n×m operates on a column vector of dimension m×1 to produce a row vector of dimension 1×n.