Matrices are arrays of numbers in rows and columns. In running text, an overall symbol can be used (eg matrix Y), or general symbols or vectors can be used to represent the components of the matrix.
\(M=\left[\begin{matrix}\mathbf{a}&\mathbf{b}&\mathbf{c}\end{matrix}\right]\) becomes \[M=\left[\begin{matrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{matrix}\right]\]
where \[\mathbf{a}=\left[\begin{matrix}a_1\\a_2\\a_3\end{matrix}\right],\qquad \mathbf{b}=\left[\begin{matrix}b_1\\b_2\\b_3\end{matrix}\right],\qquad \mathbf{c}=\left[\begin{matrix}c_1\\c_2\\c_3\end{matrix}\right]\]
[the matrix consists of vectors \(\mathbf{a}\), \(\mathbf{b}\) and \(\mathbf{c}\), each with components as noted]
\(M=\left[m_{ij}\right]\) becomes \[M=\left[ \begin{matrix}m_{11}&m_{12}&m_{13}\\m_{21}&m_{22}&m_{23}\end{matrix} \right]\]
[the matrix consists of elements \(m_{ij}\), where \(i\) gives the row number and \(j\) the column]
Did you know? In mathematics, the plural of matrix is matrices (not matrixes).
A matrix that is only 1 line (1 × n) or 1 column (n × 1) is known as a vector; (1 × n) matrices are also sometimes called row vectors or covectors.
