Monomial transformation

A linear map $𝑓 : 𝕂 𝑛 \to 𝕂 𝑛$ is termed monomial iff each of its components $(𝑓 𝑖) 𝑛 𝑖 = 1$ is monomial in the variables $(𝑥 𝑖) 𝑛 𝑖 = 1$ with no two components containing the same variable. linalg Equivalently, the matrix $𝑓$ is a ^diagonal transformation¹ followed by a permutation. Clearly a monomial transformation is a Linear isomorphism.