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Matrix addition

The binary operation, defined in terms of vector addition,

\[\begin{align*}
  A + B
  & =
  \begin{pmatrix}
    \vphantom{\bigg(}
    \vec{a}_1 & \cdots & \vec{a}_n
  \end{pmatrix}
  +
  \begin{pmatrix}
    \vphantom{\bigg(}
    \vec{b}_1 & \cdots & \vec{b}_n
  \end{pmatrix}
  \\[1ex]
  & =
  \begin{pmatrix}
    \vphantom{\bigg(}
    \vec{a}_1 + \vec{b}_1 & \cdots & \vec{a}_n + \vec{b}_n
  \end{pmatrix}
\end{align*}
\]

with

\[\begin{equation*}
  A_{m \times n}, B_{m \times n},
\end{equation*}
\]

where	\(A, B\)	are the terms and
	\(A + B\)	is the sum.

• Properties