Monotonically positive matrices

A matrix A is monotonically positive (MP) if there exists a matrix U   such that A=UUTA=UUT and each column of U is monotonically nonincreasing or nondecreasing. Following the approach in J. Nie (2014) [15], we propose a semidefinite algorithm for checking whether or not a matrix is MP. If it is not MP, a certificate for it can be obtained; if it is MP, an MP-decomposition can be obtained. Some computational experiments are presented to show how to do this.