Matrix Addition
Overview
Matrix addition between matrices of the same dimensions (same number of rows and columns)
can be defined in a simple manner.
For a matrix with entries {% a_{ij} %} and another matrix with entries {% b_{ij} %}
the elements of the sum is defined to be {% c_{ij} = a_{ij} + b_{ij} %}
{%
\begin{bmatrix}
c_{11} & c_{12} & c_{13} \\
c_{21} & c_{22} & c_{23}\\
c_{31} & c_{32} & c_{33} \\
\end{bmatrix}
=
\begin{bmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23}\\
a_{31} & a_{32} & a_{33} \\
\end{bmatrix}
+
\begin{bmatrix}
b_{11} & b_{12} & b_{13} \\
b_{21} & b_{22} & b_{23}\\
b_{31} & b_{32} & b_{33} \\
\end{bmatrix}
%}
=
\begin{bmatrix}
a_{11}+b_{11} & a_{12}+b_{12} & a_{13}+b_{13} \\
a_{21}+b_{21} & a_{22}+b_{22} & a_{23}+b_{23}\\
a_{31}+b_{31} & a_{32}+b_{32} & a_{33}+b_{33} \\
\end{bmatrix}
