A calculus of the absurd

18.1.2 Adding matrices

Adding matrices is fairly straightforward - we just add all elements in the same position in the matrices we are adding (this does imply, however, that we can only add together matrices which are of the same size).

\begin{equation} (A)_{ij} + (B)_{ij} = (A + B)_{ij} \end{equation}

For example, to add

\begin{equation} \begin{pmatrix} 1 & 2 \\ 5 & 12 \end {pmatrix} + \begin{pmatrix} 3 & 5 \\ 6 & 7 \end {pmatrix} \end{equation}

We just add the first item of the first row of the first matrix with the first item of the first row of the second matrix and so on...

\begin{equation} \begin{pmatrix} 1 & 2 \\ 5 & 12 \end {pmatrix} + \begin{pmatrix} 3 & 5 \\ 6 & 7 \end {pmatrix} = \begin{pmatrix} 4 & 7 \\ 11 & 19 \end {pmatrix} \end{equation}