Linear Substitution

the replacement of the variables x₁, x₂,..., x_m by the variables y₁, y₂,..., y_n according to the formulas

x_i = a_i1y₁ + a_i2y₂ + ⋯ + a_iny_n

where i = 1, 2, ..., m and the a_ij are constants. Linear transformations and coordinate changes in vector spaces reduce to linear substitutions.