Chapter 2: Operations with Matrices

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, $$C_{ij}=\lambda A_{ij}$$ where $\lambda$ is a scalar, that is, a complex number. For example, if $$A = \left(\begin{array}{cc} a&b\\ c&d\\ \end{array} \right),$$ then $$3A=3\cdot \left(\begin{array}{cc} a&b\\ c&d\\ \end{array} \right) = \left(\begin{array}{cc} 3a&3b\\ 3c&3d\\ \end{array} \right).$$

Try it for yourself by computing $$i\cdot \left(\begin{array}{cc} 1&i\\ -2i&3\\ \end{array} \right).$$


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