How to compute the image of a polytope after a linear transformation (formal proof) ?
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I have been looking for a result with (formal proof) of the following question (exactly the same question as posed in https://mathoverflow.net/questions/179282/mathcalh-polyhedron-under-a-linear-map?noredirect=1&lq=1):
Let $P={x∈R^n∣Ax≤b}$ be a (bounded) polyhedron for $A∈R^{m×n}$ and $b∈R^m$, n,m>0.
Moreover, let $M:R^n→R^p$ be a linear map for $p≤n$.
I'm interested in computing a H-representation of $M⋅P={Cx∣x∈P}$
Also asked in: How to compute the image of a polyhedron under a linear transformation. Although the two first answers (switching to v-representation and then back to h-representation seems intuitively correct), is there anywhere I could find a formal proof of this?
Thank you all very much
linear-algebra convex-analysis polytopes
asked Nov 13 at 18:47
Taiwaninja
113
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up vote
0
down vote
favorite
I have been looking for a result with (formal proof) of the following question (exactly the same question as posed in https://mathoverflow.net/questions/179282/mathcalh-polyhedron-under-a-linear-map?noredirect=1&lq=1):
Let $P={x∈R^n∣Ax≤b}$ be a (bounded) polyhedron for $A∈R^{m×n}$ and $b∈R^m$, n,m>0.
Moreover, let $M:R^n→R^p$ be a linear map for $p≤n$.
I'm interested in computing a H-representation of $M⋅P={Cx∣x∈P}$
Also asked in: How to compute the image of a polyhedron under a linear transformation. Although the two first answers (switching to v-representation and then back to h-representation seems intuitively correct), is there anywhere I could find a formal proof of this?
Thank you all very much
linear-algebra convex-analysis polytopes
asked Nov 13 at 18:47
Taiwaninja
113
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have been looking for a result with (formal proof) of the following question (exactly the same question as posed in https://mathoverflow.net/questions/179282/mathcalh-polyhedron-under-a-linear-map?noredirect=1&lq=1):
Let $P={x∈R^n∣Ax≤b}$ be a (bounded) polyhedron for $A∈R^{m×n}$ and $b∈R^m$, n,m>0.
Moreover, let $M:R^n→R^p$ be a linear map for $p≤n$.
I'm interested in computing a H-representation of $M⋅P={Cx∣x∈P}$
Also asked in: How to compute the image of a polyhedron under a linear transformation. Although the two first answers (switching to v-representation and then back to h-representation seems intuitively correct), is there anywhere I could find a formal proof of this?
Thank you all very much
linear-algebra convex-analysis polytopes
asked Nov 13 at 18:47
Taiwaninja
113
I have been looking for a result with (formal proof) of the following question (exactly the same question as posed in https://mathoverflow.net/questions/179282/mathcalh-polyhedron-under-a-linear-map?noredirect=1&lq=1):
Let $P={x∈R^n∣Ax≤b}$ be a (bounded) polyhedron for $A∈R^{m×n}$ and $b∈R^m$, n,m>0.
Moreover, let $M:R^n→R^p$ be a linear map for $p≤n$.
I'm interested in computing a H-representation of $M⋅P={Cx∣x∈P}$
Also asked in: How to compute the image of a polyhedron under a linear transformation. Although the two first answers (switching to v-representation and then back to h-representation seems intuitively correct), is there anywhere I could find a formal proof of this?
Thank you all very much
linear-algebra convex-analysis polytopes
linear-algebra convex-analysis polytopes
asked Nov 13 at 18:47
Taiwaninja
113
asked Nov 13 at 18:47
Taiwaninja
113
asked Nov 13 at 18:47
Taiwaninja
113
asked Nov 13 at 18:47
Taiwaninja
113
asked Nov 13 at 18:47
Taiwaninja
113
113
add a comment |
add a comment |
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