Homogenous Linear System

Last updated Nov 1, 2022

Let $F$ be a Field, let $n, m \in \mathbb{N}$. Then we call an Equation System of the form

$$\begin{align*} a_{11} x_{1} + \dots a_{1n} x_{n} &= 0\\ .\\ .\\ .\\ a_{m1} x_{1} + \dots a_{mn} x_{n} &= 0 \end{align*}$$ a Homogenous Linear System of the Equation Variables $x_{1}, \dots, x_{n}$.

Let $V, W$ be Vector Spaces over Field $F$. A Homogenous Linear System from $V$ to $W$ is a Linear Equation System that is also a Homogenous Equation System.

1. Definition 1 is the usual definition seen in books and on the internet, while definition 2 is my more general definition.