= Matrix-vector product
{title2=$(Ax)_i=\sum_jA_{ij}x_j$}
For an $m$-by-$n$ <matrix> $A$ and an $n$-component column <vector> $x$, their <matrix-vector product> is the column <vector> with entries
$$
(Ax)_i=\sum_{j=1}^n A_{ij}x_j.
$$
Equivalently, 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>.
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