Nullity

Nullity, in linear algebra, refers to the dimension of a matrix's null space—the set of all vectors that, when multiplied by the matrix, result in the zero vector. Essentially, it measures the number of independent directions in which the matrix "kills" the input, indicating how many degrees of freedom lead to zero output. Nullity helps understand the solutions to homogeneous equations and relates to the matrix's rank through the Rank-Nullity Theorem, which states that the sum of a matrix's rank and nullity equals the number of its columns.