Definition:Homogeneous Linear Equations

Definition
A system of homogeneous linear equations is a set of simultaneous linear equations:


 * $\displaystyle \forall i \in \left[{1 .. m}\right] : \sum_{j=1}^n \alpha_{i j} x_j = \beta_i$

such that all the $\beta_i$ are equal to zero:


 * $\displaystyle \forall i \in \left[{1 .. m}\right] : \sum_{j=1}^n \alpha_{i j} x_j = 0$

That is: