MathDB

Let

n

be a positive integer. What is the largest

k

for which there exist

n\times n

matrices

M_1,\dots,M_k

and

N_1,\dots,N_k

with real entries such that for all

i

and

j,

the matrix product

M_iN_j

has a zero entry somewhere on its diagonal if and only if

i\ne j?

Problem Statement