On Lei, Miranda, and Thompsonʹs result on singular values and diagonal elements

Thomspon and Singʹs result on the singular values and the diagonal elements of a complex n × n matrix has been recently extended to arbitrary m matrices, by Lei and by Miranda and Thompson independently. The real case in which the determinant of the product of the m real matrices is nonnegative (or nonpositive) was raised by Miranda and Thompson. In this note, we provide an answer to the question, and we also extend some other results of Lei.