> [!summary] Vector addition and scalar multiplication are two assumptions in valid operations. >[!info]+ Read Time **⏱ 1 min** # Definition Vector addition is another assumption that you can add any two vectors. So if $\vec{u},\vec{v}$ were two vectors, then the following operation is valid $ \vec{u}+\vec{v} $ Scalar multiplication is the assumption that you can multiply any [[Scalar & Vectors|scalar]] amount by a [[Scalar & Vectors|vector]]. The scalar can be any number, for example, a number from [[Real Numbers|real number]]. If $k$ represented a [[Scalar & Vectors|scalar]] number and $\vec{u}$ was a vector, then the following operation is valid: $ k \vec{u} $