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Mathbuff
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Let $S$ denote the set of all complex non-negative definite matrices with all diagonal elements being less that or equal to one. Can we show that any matrix which belongs to the set of all non-zero extreme points of $S$ has all its diagonal elements equal to zero or one?

Let $S$ denote the set of all complex non-negative definite matrices with all diagonal elements being less that or equal to one. Can we show that any matrix which belongs to the set of all non-zero extreme points of $S$ has all its diagonal elements equal to one?

Let $S$ denote the set of all complex non-negative definite matrices with all diagonal elements being less that or equal to one. Can we show that any matrix which belongs to the set of all non-zero extreme points of $S$ has all its diagonal elements equal to zero or one?

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Mathbuff
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Let $S$ denote the set of all complex non-negative definite matrices with all diagonal elements being less that or equal to one. Can we show that any matrix which belongs to the set of all non-zero extreme points of $S$ has all its diagonal elements equal to one?

Let $S$ denote the set of all complex non-negative definite matrices with all diagonal elements being less that or equal to one. Can we show that any matrix which belongs to the set of extreme points of $S$ has all its diagonal elements equal to one?

Let $S$ denote the set of all complex non-negative definite matrices with all diagonal elements being less that or equal to one. Can we show that any matrix which belongs to the set of all non-zero extreme points of $S$ has all its diagonal elements equal to one?

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Mathbuff
Mathbuff
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Extreme points of a convex set

Let $S$ denote the set of all complex non-negative definite matrices with all diagonal elements being less that or equal to one. Can we show that any matrix which belongs to the set of extreme points of $S$ has all its diagonal elements equal to one?