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.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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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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