TITLE: What are the linear isometries on $R^n$, equipped with the $l_1$ norm?
QUESTION [5 upvotes]: Which conditions must the matrix entries satisfy, and what would be an interpretation of the row and column sums of the matrix?

REPLY [5 votes]: Hint: Such an isometry would have to map the $l^1$-unit-sphere onto itself. How does this "sphere" look like?