conic hull of a set of points in terms of intersection of half spaces
Convex cones can be characterized in two ways, one as a conic hull of a set of points. Let $mathbf{X}$ is a $ntimes n$ matrix where each column is a vector, then $coni(mathbf{X})$ defines a convex cone.
Is it possible to represent this in the intersection of the half space form ${y | mathbf{A}y geq 0}$. I read that if $mathbf{X}$ is invertible then $coni(mathbf{X}) = {y|mathbf{X}^{-1}y geq 0}$. Is it correct ?. If yes, how can I show this ?
convex-analysis convex-hulls convex-cone
asked Dec 9 at 12:59
Shew
563413
add a comment |
Convex cones can be characterized in two ways, one as a conic hull of a set of points. Let $mathbf{X}$ is a $ntimes n$ matrix where each column is a vector, then $coni(mathbf{X})$ defines a convex cone.
Is it possible to represent this in the intersection of the half space form ${y | mathbf{A}y geq 0}$. I read that if $mathbf{X}$ is invertible then $coni(mathbf{X}) = {y|mathbf{X}^{-1}y geq 0}$. Is it correct ?. If yes, how can I show this ?
convex-analysis convex-hulls convex-cone
asked Dec 9 at 12:59
Shew
563413
Fourier-Motzkin elimination? en.wikipedia.org/wiki/Fourier%E2%80%93Motzkin_elimination
– Lord Shark the Unknown
Dec 9 at 13:08
add a comment |
Convex cones can be characterized in two ways, one as a conic hull of a set of points. Let $mathbf{X}$ is a $ntimes n$ matrix where each column is a vector, then $coni(mathbf{X})$ defines a convex cone.
Is it possible to represent this in the intersection of the half space form ${y | mathbf{A}y geq 0}$. I read that if $mathbf{X}$ is invertible then $coni(mathbf{X}) = {y|mathbf{X}^{-1}y geq 0}$. Is it correct ?. If yes, how can I show this ?
convex-analysis convex-hulls convex-cone
asked Dec 9 at 12:59
Shew
563413
Convex cones can be characterized in two ways, one as a conic hull of a set of points. Let $mathbf{X}$ is a $ntimes n$ matrix where each column is a vector, then $coni(mathbf{X})$ defines a convex cone.
Is it possible to represent this in the intersection of the half space form ${y | mathbf{A}y geq 0}$. I read that if $mathbf{X}$ is invertible then $coni(mathbf{X}) = {y|mathbf{X}^{-1}y geq 0}$. Is it correct ?. If yes, how can I show this ?
convex-analysis convex-hulls convex-cone
convex-analysis convex-hulls convex-cone
asked Dec 9 at 12:59
Shew
563413
asked Dec 9 at 12:59
Shew
563413
asked Dec 9 at 12:59
Shew
563413
asked Dec 9 at 12:59
Shew
563413
asked Dec 9 at 12:59
Shew
563413
563413
Fourier-Motzkin elimination? en.wikipedia.org/wiki/Fourier%E2%80%93Motzkin_elimination
– Lord Shark the Unknown
Dec 9 at 13:08
add a comment |
Fourier-Motzkin elimination? en.wikipedia.org/wiki/Fourier%E2%80%93Motzkin_elimination
– Lord Shark the Unknown
Dec 9 at 13:08
Fourier-Motzkin elimination? en.wikipedia.org/wiki/Fourier%E2%80%93Motzkin_elimination
– Lord Shark the Unknown
Dec 9 at 13:08
Fourier-Motzkin elimination? en.wikipedia.org/wiki/Fourier%E2%80%93Motzkin_elimination
– Lord Shark the Unknown
Dec 9 at 13:08
add a comment |
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Fourier-Motzkin elimination? en.wikipedia.org/wiki/Fourier%E2%80%93Motzkin_elimination
– Lord Shark the Unknown
Dec 9 at 13:08