rank-nullity theorem

English

Noun

rank-nullity theorem (uncountable)

1. (linear algebra) A theorem about linear transformations (or the matrices that represent them) stating that the rank plus the nullity equals the dimension of the entire vector space (which is the linear transformation’s domain).

   If — for a homogeneous system of linear equations — there are V unknowns and R (linearly independent) equations then, according to the rank-nullity theorem, the solution space is N equals V − R dimensional.