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Matrix

a.k.a.

Define

… in terms of vectors as the rectangular array

\[\begin{equation*}
  A
  =
  A_{m \times n}
  =
  \begin{pmatrix}
    \vphantom{\Big(}
    \vec{a_1} & \cdots & \vec{a_n}
  \end{pmatrix}
  =
  \begin{pmatrix}
    a_{11} & \cdots & a_{1n} \\
    \vdots & \ddots & \vdots \\
    a_{m1} & \cdots & a_{mn}
  \end{pmatrix},
\end{equation*}
\]

where	\(\vec{a}_j\)	is the \(j\)-th column vector and
	\(a_{ij}\)	is the entry in \(i\)-th row and \(j\)-th column.

Denote

… as shown above or:

• with square brackets instead of parentheses: \(A = \begin{bmatrix} \vphantom{\big(} \ldots \end{bmatrix}\)
• with comma-separated indices: \(a_{i, j}\)

• Zero matrix
• Matrix addition
• Matrix scaling