The null space property (NSP) is a property of matrices that arises in compressed sensing and sparse signal recovery.
A matrix A satisfies the null space property if the only sparse vector x (i.e., a vector with few non-zero entries) that satisfies Ax = 0 is the zero vector. In other words, if the null space of A contains only the zero vector, then A satisfies the null space property.
This property is important in compressed sensing because it implies that if a sparse signal x is measured by a linear measurement system described by A, then the measurements are sufficient to recover x exactly with high probability. This is because any sparse vector that is not equal to x would have a non-zero measurement error and would not satisfy the null space property.
Reference: https://chat.openai.com/chat