Algebraic rules for matrix addition and scalar multiplication

Summary

• \(A,B,C\) are \(n×m\) matrices, \(α,β\) are scalars.
• \(A+B=B+A\)
• \(αA=Aα\)
• \((A+B)+C=A+(B+C)\)
• \((αβ)A=α(βA)\)
• \((α+β)A=αA+βA\)
• \(α(A+B)=αA+αB\)
• \(αA+βB\) is called a linear combination of \(A\) and \(B\) .