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Matrix multiplication

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.

• Anti-definition
• Properties
• Anti-properties
• Example
• Synonyms