  These notes are motivated by the work of Jean-Paul Cardinal on symmetric
matrices related to the Mertens function. He showed that certain norm bounds on
his matrices implied the Riemann hypothesis. Using a different matrix norm we
show an equivalence of the Riemann hypothesis to suitable norm bounds on his
matrices in the new norm. Then we specify a deformed version of his Mertens
function matrices that unconditionally satisfies a norm bound that is of the
same strength as his Riemann hypothesis bound.
