Matrix-vector product ($(Ax{)}_i={\sum }_j{A}_{ij}{x}_j$)

For an $m$-by-$n$ matrix $A$ and an $n$-component column vector $x$, their matrix-vector product is the column vector with entriesEquivalently, it is the linear combination of the columns of $A$ with coefficients $x_j$. This formula uses no complex conjugation, so over the complex numbers it should not be confused with an inner product of a row and $x$. A dense evaluation costs $O(mn)$ arithmetic operations in Big O notation.