Matrix Equation System

Last updated Nov 1, 2022

Let $F$ be a Field. And consider a Finite Equation System of order $m$ $$f_{i}(\mathbf{x}) = b_{i} \text{ }i \in [m]$$ for ${f_{i} \in F^{F^{n}}}{i \in [m]}, {b{i} \in F}{i \in [m]}$. Then, it is a Matrix Equation System there exists some Matrix $A \in F^{m \times n}$ so that the Equation System $$A \mathbf{x} = \mathbf{b}$$ for $\mathbf{b} = (b{1}, \dots, b_{m}) \in F^{m}$ with the same Solution Set.

1. We usually just represent a Matrix Equation System in terms of its Matrix and Equation System Constants.

• Matrix Multiplication