The 1 matrix norm, denoted as $\|A\|_1$, of a matrix $A$ is defined as the maximum absolute column sum of the matrix. Mathematically, if $A$ is an $m \times n$ matrix with elements $a_{ij}$, then
\[
\|A\|_1 = \max_{1 \leq j \leq n} \sum_{i=1}^m |a_{ij}|.
\]
This
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