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...Projective geometry lecture notes thomas baird march contents introduction vector spaces and their duals fields subspaces matrices dual homogeneous coordinates visualizing space linear two points determine a line planar lines intersect at point transformations the erlangen program versus examples of direct sums general position cross ratio classical theorems desargues theorem pappus duality quadrics conics ane algebraic sets bilinear quadratic forms change basis digression on hessian rational parametrization circle ruled surfaces polars pencils degeneration exterior algebras multilinear algebra grassmanian pluc ker embedding decomposability vectors set in ideas for projects has its origins renaissance italy development perspective painting problem capturing dimensional image canvas it is familiar fact that objects appear smaller as they get farther away apparent angle between straight depends vantage observer more euclidean not well equipped to make sense this because length are dened ...