Linear Combination

Definition

A sum of the form $α_{1} | v_{1} ⟩ + α_{2} | v_{2} ⟩ + \dots + α_{n} | v_{n} ⟩$ , where $α_{i}$ are scalars, is called a linear combination of $| v_{1} ⟩, | v_{2} ⟩, \dots, | v_{n} ⟩$ .