A linear combination of matrix columns using a vector of weights,

\begin{align*} AB & = A \begin{pmatrix} \vphantom{\bigg(} \vec{b}_1 & \cdots & \vec{b}_n \end{pmatrix} = \begin{pmatrix} \vphantom{\bigg(} A \vec{b}_1 & \cdots & A \vec{b}_n, \end{pmatrix} \in V^m \\ \qusing* A \vec{b} & = \begin{pmatrix} \vphantom{\bigg(} \vec{a}_1 & \cdots & \vec{a}_n \end{pmatrix} \begin{pmatrix} b_1 \\ \vdots \\ b_m \end{pmatrix} = b_1 \vec{a}_1 + \cdots + b_m \vec{a}_n \in V^m, \end{align*}

defined in terms of vector addition and scalar multiplication,

where	\(A_{m \times p}, B_{p \times n}\)	are the factors,
	\((AB)_{m \times n}\)	is the resulting product,
	\(V^m\)	is the containing vector space.

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