Overview
The notion of a matrix limit extends the concept from analysis of a limit to matrices.
Given an infinite sequence of {% n \times m %} matrices {% A_i %} where {% i \in \{0,1,2,... \} %}, the sequence is said to converge to the matrix {% A %} if the sequence {% a_{ijk} %} converges as {% k \rightarrow \infty %} where {% a_{ijk} %} is the {% i,j %} element of the {% k^{th} %} matrix
Sums
Given an infinite sequence of {% n \times m %} matrices {% A_i %} where {% i \in \{0,1,2,... \} %}, the sum {% \sum_{i=0}^\infty A_i %} is said to converge to the matrix {% A %} if
{% \sum_k a_{ijk} %}
converges
where {% a_{ijk} %} is the {% i,j %} element of the {% k^{th} %} matrix