Definition:Trivial Solution to Homogeneous Simultaneous Linear Equations

Definition
Let $S$ be a system of homogeneous simultaneous linear equations:


 * $\displaystyle \forall i \in \set {1, 2, \ldots, m}: \sum_{j \mathop = 1}^n \alpha_{i j} x_j = 0$

The solution:
 * $\tuple {x_1, x_2, \ldots, x_n}$

such that:
 * $\forall j \in \set {1, 2, \ldots, n}: x_j = 0$

is known as the trivial solution to $S$.

Also see

 * Trivial Solution to System of Homogeneous Simultaneous Linear Equations is Solution