matrix multiplication

if $\text{[math]}$ is an $\text{[math]}$ matrix whose $\text{[math]}$ th entry is $\text{[math]}$ , and $\text{[math]}$ is an $\text{[math]}$ matrix whose $\text{[math]}$ th entry is $\text{[math]}$ , then $\text{[math]}$ is the $\text{[math]}$ matrix with entries
$\text{[math]}$ [cite:;taken from @calc_hubbard_2015 definition 1.2.4]

$\text{[math]}$

broken link: attachment:matrix-multiplication.gif

matrices can be multiplied by constants, let $\text{[math]}$ be a matrix and $\text{[math]}$ be a constant, the definition of such multiplication is:
$\text{[math]}$