Abstract
Part 1 Linear algebra over division rings: matrices over division rings matrix representations of subspaces systems of linear equations. Part 2 Affine geometry and projective geometry: affine spaces and affine groups projective spaces and projective groups one-dimensional projective geometry. Part 3 Geometry of rectangular matrices: the space of rectangular matrices proof of the fundamental theorem application to graph theory. Part 4 Geometry of alternate matrices: the space of alternate matrices maximal sets. Part 5 Geometry of symmetric matrices: the space of symmetric matrices proof of the fundamental theorem I-III. Part 6 Geometry of hermitian matrices: maximal sets of rank 1 proof of the fundamental theorem (the case n is greater than or equal to 3) the maximal set of rank 2 (n=2) proof of the fundamental theorem (the case n=2) and others.
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