Let \({\bf{x}}\) be an \(m \times n\) matrix.
The formula used to compute the norm is \(\left\| {\bf{x}} \right\|_1 = \mathop {\max }\limits_{1 \le j \le n} \sum\limits_{i = 1}^m {\left| {x_{i,j} } \right|} \).
This is merely the maximum absolute column sum of the \(m \times n\) maxtris.
References
Bellman, R. (1987). Matrix Analysis, Second edition, Classics in Applied Mathematics,
Society for Industrial and Applied Mathematics.
Golub, G. H. and C. F. Van Loan (1996). Matrix Computations, Third Edition, The John
Hopkins University Press.
Horn, R. A. and C. R. Johnson (1985). Matrix Analysis, Cambridge University Press.