 Restricted isometry property

The restricted isometry property controls $\Vert Ax{\Vert }_2^2/\Vert x{\Vert }_2^2$ uniformly over sparse vectors. It supplies quantitative near-orthogonality of disjoint sparse coordinate combinations, not merely normalization of individual columns.

The Restricted Isometry Property (RIP) is a concept from the field of compressed sensing and high-dimensional geometry. It describes a condition under which a linear transformation approximately preserves the distances between a limited number of vectors in a high-dimensional space.