Sum of matrices and product by a scalar

The first operations on matrices are the simplest: they are carried out element by element.

Property — Sum and product by a scalar

$(A+B)_{ij}=a_{ij}+b_{ij}$ for matrices of the same dimensions; $(\alpha A)_{ij}=\alpha\,a_{ij}$ for every $\alpha\in\mathbb{R}$. The sum is commutative and associative; the neutral element is the matrix of all zeros.

Connections

Topics: Linear systems
Concepts: Matrix · Sum of matrices
Skills: Computing