Let A S n + be a symmetric, positive semi-definite matrix. 1. Show that the trace,

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Let A ∈ Sⁿ₊be a symmetric, positive semi-definite matrix.

1. Show that the trace, trace A, and the Frobenius norm,ΙΙAΙΙ_F,de-pend only its eigenvalues, and express both in terms of the vector of eigenvalues.

2. Show that

3. Identify classes of matrices for which the corresponding lower bound on the rank is attained.

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Optimization Models

ISBN: 9781107050877

1st Edition

Authors: Giuseppe C. Calafiore, Laurent El Ghaoui

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Question Posted: Aug 09, 2023 07:04 AM

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Let A S n + be a symmetric, positive semi-definite matrix. 1. Show that the trace,

Question:

(trace A)² ≤ rank(A)||A||} .

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Optimization Models

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