Suppose that $\complex{m}$ is the set of column vectors of size $m$ (Definition VSCV) with addition and scalar multiplication as defined in Definition CVA and Definition CVSM. Then

• ACC Additive Closure, Column Vectors
  If $\vect{u},\,\vect{v}\in\complex{m}$, then $\vect{u}+\vect{v}\in\complex{m}$.
  
  
• SCC Scalar Closure, Column Vectors
  If $\alpha\in\complex{\null}$ and $\vect{u}\in\complex{m}$, then $\alpha\vect{u}\in\complex{m}$.
  
  
• CC Commutativity, Column Vectors
  If $\vect{u},\,\vect{v}\in\complex{m}$, then $\vect{u}+\vect{v}=\vect{v}+\vect{u}$.
  
  
• AAC Additive Associativity, Column Vectors
  If $\vect{u},\,\vect{v},\,\vect{w}\in\complex{m}$, then $\vect{u}+\left(\vect{v}+\vect{w}\right)=\left(\vect{u}+\vect{v}\right)+\vect{w}$.
  
  
• ZC Zero Vector, Column Vectors
  There is a vector, $\zerovector$, called the zero vector, such that $\vect{u}+\zerovector=\vect{u}$ for all $\vect{u}\in\complex{m}$.
  
  
• AIC Additive Inverses, Column Vectors
  If $\vect{u}\in\complex{m}$, then there exists a vector $\vect{-u}\in\complex{m}$ so that $\vect{u}+ (\vect{-u})=\zerovector$.
  
  
• SMAC Scalar Multiplication Associativity, Column Vectors
  If $\alpha,\,\beta\in\complex{\null}$ and $\vect{u}\in\complex{m}$, then $\alpha(\beta\vect{u})=(\alpha\beta)\vect{u}$.
  
  
• DVAC Distributivity across Vector Addition, Column Vectors
  If $\alpha\in\complex{\null}$ and $\vect{u},\,\vect{v}\in\complex{m}$, then $\alpha(\vect{u}+\vect{v})=\alpha\vect{u}+\alpha\vect{v}$.
  
  
• DSAC Distributivity across Scalar Addition, Column Vectors
  If $\alpha,\,\beta\in\complex{\null}$ and $\vect{u}\in\complex{m}$, then $(\alpha+\beta)\vect{u}=\alpha\vect{u}+\beta\vect{u}$.
  
  
• OC One, Column Vectors
  If $\vect{u}\in\complex{m}$, then $1\vect{u}=\vect{u}$.