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AM-HM and Nesbitt Inequalities for Hermitian Positive Definite Matrices
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Notes:
About Hermitian positive definite and positive semidefinite matrices (starting on page 15):
2:55 proof of the arithmetic mean harmonic mean inequality and Nesbitt’s inequality for scalars
7:35 AB and BA share the same nonzero eigenvalues
9:40 The eigenvalues of Hermitian positive definite and positive definite matices
12:08 The main lemma used to obtain the inequalities: if A is an nxn Hermitian positive definite matrix then the 2nx2n block matrix with 4 blocks A, I_{nxn}; I_{n,x} A^-1 is positive semidefinite
14:40 The main proof
Reference:
About Hermitian positive definite and positive semidefinite matrices (starting on page 15):
2:55 proof of the arithmetic mean harmonic mean inequality and Nesbitt’s inequality for scalars
7:35 AB and BA share the same nonzero eigenvalues
9:40 The eigenvalues of Hermitian positive definite and positive definite matices
12:08 The main lemma used to obtain the inequalities: if A is an nxn Hermitian positive definite matrix then the 2nx2n block matrix with 4 blocks A, I_{nxn}; I_{n,x} A^-1 is positive semidefinite
14:40 The main proof
Reference:
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