Matrix-Vector Product

linear-algebra

Definition

Matrix-Vector Product

Let $A\in F^{m\times n}$ be a matrix and $x\in F^n$ a vector over a field $F$. The matrix-vector product is the operation

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

defined by

$$(Ax{)}_i=\sum _{j=1}^n{A}_{ij}{x}_j$$

for all $1\le i\le m$.

Einstein Notation: $(Ax{)}_i=A_{ij}{x}_j\in F^m$