[[Linear algebra MOC]]
# Monomial transformation

A [[linear map]] $f : \mathbb{K}^n \to \mathbb{K}^n$ is termed **monomial** iff each of its components $(f_i)_{i=1}^n$ is monomial in the variables $(x_i)_{i=1}^n$ with no two components containing the same variable. #m/def/linalg 
Equivalently, the matrix $f$ is a [[Types of square matrix#^diagonal]] transformation[^ie] followed by a permutation.
Clearly a monomial transformation is a [[Linear isomorphism]].

  [^ie]: i.e. a transformation represented by a diagonal matrix.

#
---
#state/tidy | #lang/en | #SemBr