Simple formula derivation notes (1)-Rayleigh entropy

Please deduce that the upper and lower bounds of Rayleigh entropy are the minimum and maximum eigenvalues ​​of R.

Answer: Set

the eigenvalues ​​(real numbers) of the real symmetric matrix R in order of magnitude, and set the

corresponding orthonormal eigenvector system to

any value 0≠ x ∈ R ^n- , the

so there

makes

it

and

thus be available

Easy to verify

Therefore