Projective space is a fundamental concept in both mathematics and geometry, particularly in the fields of projective geometry and algebraic geometry. It can be intuitively thought of as an extension of the concept of Euclidean space. Here are some key points to understand projective space: ### Definition 1.
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Projective space is the set of one-dimensional subspaces of a vector space of dimension , written in homogeneous coordinates .
The definition is to take the vector space, remove the zero element, and identify all elements that lie on the same line, i.e.
The most important initial example to study is the real projective plane.