Question: Let A S n be positive semidefinite. Prove that Distinguish the cases det A = 0 and det A 0. In the latter

Let A ∈ Sⁿbe positive semidefinite. Prove that

n det A ii. i=1

Distinguish the cases det A = 0 and det A ≠ 0. In the latter case, consider the normalized matrix , where D = diag and use the geometric/arithmetic mean inequality.

n det A ii. i=1

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