How can I find all binary matrices $A$ such that $A^3$ is a non-negative, integer square matrix and
$$\mbox{diag}\left(A^3\right)=b$$
for some given vector $b$? Is there a way to characterize all the solutions?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.
Sign up to join this communityHow can I find all binary matrices $A$ such that $A^3$ is a non-negative, integer square matrix and
$$\mbox{diag}\left(A^3\right)=b$$
for some given vector $b$? Is there a way to characterize all the solutions?
A is a matrix with the same eigenvectors as B and with eigenvalues that are the cube roots of B's eigenvalues