Abstract Algebra: Theory and Applications · Problem 11.4.3

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · matrix-multiplication-homomorphism

Problem

Let

A

be an

m \times n

matrix. Show that matrix multiplication,

x \mapsto Ax

, defines a homomorphism

\phi : \mathbb{R}^n \to \mathbb{R}^m