Scalar-Matrix Multiplication

linear-algebra

Definition

Scalar-Matrix Multiplication

Let $A\in F^{m\times n}$ be a matrix over a field $F$ and $\lambda \in F$ a scalar. Scalar-matrix multiplication is the entrywise operation

$$\cdot :F\times F^{m\times n}\to F^{m\times n}.$$

Einstein Notation: $(\lambda A{)}_{ij}=\lambda A_{ij}\in F^{m\times n}$