2020/05/22 by André L. G. Mandolesi, Mandolesi, André L. G. · 1 citation
Mathematics · Computer Science · Physics and Astronomy · #Algebraic and Geometric Analysis #Matrix Theory and Algorithms #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2005.12700
Grassmann angles improve upon similar concepts of angle between subspaces that measure volume contraction in orthogonal projections, working for real or complex subspaces, and being more efficient when dimensions are different. Their relations with contractions, inner and exterior products of multivectors are used to obtain formulas for computing these or similar angles in terms of arbitrary bases, and various identities for the angles with certain families of subspaces. These include generalizations of the Pythagorean trigonometric identity cos2θ+sin2θ=1 for high dimensional and complex subspaces, which are connected to generalized Pythagorean theorems for volumes, quantum probabilities and Clifford geometric product.