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In this paper, using Descartes law of sign, we provide elementary proof ofresults on the number of real eigenvalues of real matrices of which certainproperties on the signs of their principal minors are known. More precisely, weanalyze P, N, Q, R, PN and $QR$ matrices as well as their variants "almost","weak" and "sub-zero" matrices.

Eigenvalues of Real Matrices with Prescribed Principal Minors Sign and Descartes Law of Signs