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rank-nullity theorem

name

Definitions

  1. A theorem about linear transformations (or the matrices that represent them) stating that…

    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.

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA