06-240/Classnotes For Thursday, September 28

Linear Combination

Definition: Let (u_i) = (u₁, u₂, ..., u_n) be a sequence of vectors in V. A sum of the form

a_i $\in$ F, $\sum _{i=1}^{n}$ a_iu_i = a₁u₁ + a₂u₂+ ... +a_nu_n

is called a "Linear Combination" of the u_i.