# scalar multiplication axioms

Scalar multiplication is defined generally as a function $S:E \times E \longrightarrow K$,where $K\in(R,C)$, $E$ - linear space, for which 5 axioms are true:
$1. S(x+y,z)=S(x,z)+S(y,z)\\2. S(\lambda x,y)=\lambda S(x,y)\\3. S(x,y)=\bar {S(x,y)}\\4. S(x,x)\geq 0\\5. S(x,x)=0 \Rightarrow x=\bar{0}$