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Linear Matrix Inequalities (LMIs)

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A Matrix Inequality for positive definite matrices

Let $X$ and $Y$ be positive semi-definite self-adjoint complex matrices of same finite order. The, is it true that $|X-Y|\leq X+Y$ where for any matrix $A$, $|A|$ is defined to be $|A|:=(A^*A)^{\frac{ …
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