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Section 3.2 Scalar Multiplication

A matrix can be multiplied by a scalar, in which case each element of the matrix is multiplied by the scalar. In components,

\begin{equation} C_{ij}=\lambda A_{ij}\tag{3.2.1} \end{equation}

where \(\lambda\) is a scalar, that is, a complex number. For example, if

\begin{equation} A = \left(\begin{array}{cc} a\amp b\\ c\amp d \end{array} \right)\text{,}\tag{3.2.2} \end{equation}


\begin{equation} 3A=3\cdot \left(\begin{array}{cc} a\amp b\\ c\amp d \end{array} \right) = \left(\begin{array}{cc} 3a\amp 3b\\ 3c\amp 3d \end{array} \right)\text{.}\tag{3.2.3} \end{equation}

Try it for yourself by computing

\begin{equation} i\cdot \left(\begin{array}{cc} 1\amp i\\ -2i\amp 3 \end{array} \right)\text{.}\tag{3.2.4} \end{equation}