Questions about projective space in geometry, a space which can be seen as the set of lines through the origin in some vector space. As such it is a special case of a Grassmanian. See https://en.wikipedia.org/wiki/Projective_space
Questions tagged [projective-space]
1662 questions
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Complex projective space and its dual are homeomorphic?
Consider $\mathbb{C} P^n$ and its dual space, which consists of hyperplanes in $\mathbb{C} P^n$. Are they homeomoprhic?
I read this fact somewhere, but can't remember where. Also i don't even remember which topology must we choose for this fact to…
Elensil
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What are Desarguesian and non-Desarguesian projective spaces?
From a linear algebraic viewpoint, projective space is the set of the 1-dimensional subspaces of a vector space. Specifically, if the vector space has dimension 3 then its projective space is called a projective plane.
According to Wikipedia,…
mma
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show that $(, , )$ and $(′, ′, ′)$ define the same projective line if $(, , ) = (′, ′, ′)$ for some nonzero $ ∈ ℂ$
How do I show that the triples $(, , )$ and $(′, ′, ′)$ define the same projective line if and only if $(, , ) = (′, ′, ′)$ for some nonzero $ ∈ ℂ$
I've seen that this is the definition of a projective plane, but I don't know how to actyally prove…
user65432109
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About projective varieties
Let $f∈Κ[x_0,…,x_n]$ be a homogeneous polynomial. we define $ V(f)={p∈P^n (Κ):f(p)=0}$
is a
well-defined subset of $P^n (Κ)$. what is the meaning of well-defined ?
Mehrema
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orhogonal projection
let V be a closed subspace of L^2[0,1](i.e.,space of square Integrable functions defined on [0,1]) and let f,g ∈L^2[0,1] such that f(x)=x and g(x)=x^2. Suppose orthogonal complement of V =span {f} and P_g is the orthogonal projection of g on V,then…
MAS
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