Low Dimensions
When r = 2, the Grassmannian is the space of all planes through the origin. In Euclidean 3-space, a plane containing the origin is completely characterized by the one and only line through the origin perpendicular to that plane (and vice-versa); hence Gr(2, 3) ≅ Gr(1, 3) ≅ P2, the projective plane.
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Famous quotes containing the word dimensions:
“Is it true or false that Belfast is north of London? That the galaxy is the shape of a fried egg? That Beethoven was a drunkard? That Wellington won the battle of Waterloo? There are various degrees and dimensions of success in making statements: the statements fit the facts always more or less loosely, in different ways on different occasions for different intents and purposes.”
—J.L. (John Langshaw)
“Why is it that many contemporary male thinkers, especially men of color, repudiate the imperialist legacy of Columbus but affirm dimensions of that legacy by their refusal to repudiate patriarchy?”
—bell hooks (b. c. 1955)