## Section3.2Scalar Multiplication

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

$$C_{ij}=\lambda A_{ij}\tag{3.2.1}$$

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

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

then

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

Try it for yourself by computing

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