## Technical Report, Issue 836 |

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affine space angles between constraint beta distribution Borgwardt columns components constraint hyperplanes corresponds cosine d-dimensional subspace degree of primal denote distribution with parameters dual degeneracy expected number feasible region feasible solution Gaussian random m-1)xn Gaussian random matrix Gaussian random nxd Gaussian random vector Haar measure Hence independent inequalities inscribed balls invariant under left isometry Karmarkar's algorithm left orthogonal multiplication linear programming problem Mattheiss 24 maximum number md matrix normal random variable null space number grows number of pivot number of vertices Operations Research optimal solution orthogonal complement orthogonal to 0,0,e orthogonal transformations orthonormal nxd matrix parameters d/2 primal and dual probabilistic model random d-subspace random linear programming random m-1)xn matrix random mxn random nxd matrix random orthogonal matrix random orthonormal matrix random orthonormal nxd right orthogonal multiplication rows Schmidt and Mattheiss sign-invariant model simplex algorithm simplex method theorem 2.2 triangular with nonnegative unbounded variables vertex zero