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Felix Goldberg
Felix Goldberg
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Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B$ be the unit sphere in $n \times n$ dimensions. What is the volume of $PD_{n} \cap B$?

EDIT: Let's assume that $B$ is the unit sphere w.r.t the operator norm: $||A||=\sup_{||x||=1}{||Ax||}$.

Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B$ be the unit sphere in $n \times n$ dimensions. What is the volume of $PD_{n} \cap B$?

Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B$ be the unit sphere in $n \times n$ dimensions. What is the volume of $PD_{n} \cap B$?

EDIT: Let's assume that $B$ is the unit sphere w.r.t the operator norm: $||A||=\sup_{||x||=1}{||Ax||}$.

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Felix Goldberg
Felix Goldberg
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Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B^{n-1}$$B$ be the unit sphere in $n$$n \times n$ dimensions. What is the volume of $PD_{n} \cap B^{n-1}$$PD_{n} \cap B$?

Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B^{n-1}$ be the unit sphere in $n$ dimensions. What is the volume of $PD_{n} \cap B^{n-1}$?

Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B$ be the unit sphere in $n \times n$ dimensions. What is the volume of $PD_{n} \cap B$?

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Felix Goldberg
Felix Goldberg
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What it is the volume of the unit ball section of the cone of positive definite matrices?

Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B^{n-1}$ be the unit sphere in $n$ dimensions. What is the volume of $PD_{n} \cap B^{n-1}$?