Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

. Consider the following block matrix:

N a
aT c


where N is a m ×m real symmetric matrix, a is a m-dimensional real vector,
and c is a real scalar. Prove that the following two statements are equivalent.
i) M is a positive definite (PD) matrix.
ii) N is PD and c > a⊤N −1a.

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