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A E R"X", Q e R"Xn and Q > 0, C e R™×n. For a given X € R"Xn and X > 0, define the operator h as follows: h(X) AX A' + Q. Assume AA' > I. Prove that Tr (h(X)) > Tr(X) always holds for any X > 0.

A E R"X", Q e R"Xn and Q > 0, C e R™×n. For a given X € R"Xn and X > 0, define the operator h as follows: h(X) AX A' + Q. Assume AA' > I. Prove that Tr (h(X)) > Tr(X) always holds for any X > 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A e R"Xn, Q e R"X" and Q > 0, C e Rmxn. For a given X e R"Xn and X > 0, define the operator h as follows: h(X) AX A' + Q. Assume AA' > I. Prove that Tr(h(X)) > Tr(X) always holds for any X > 0.
Transcribed Image Text:A e R"Xn, Q e R"X" and Q > 0, C e Rmxn. For a given X e R"Xn and X > 0, define the operator h as follows: h(X) AX A' + Q. Assume AA' > I. Prove that Tr(h(X)) > Tr(X) always holds for any X > 0.
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