Two results on basic oscillatory matrices

AbstractThis paper continues the research of the authors on totally nonnegative and oscillatory matrices. First, the result of the second author stating that the Hadamard product of oscillatory tridiagonal matrices of the same order is again an oscillatory tridiagonal matrix, is extended to the class of basic oscillatory matrices introduced recently. Then it is shown that every oscillatory matrix contains a basic oscillatory matrix as a factor. This explains the role of the class of basic oscillatory matrices within the class of oscillatory matrices