Word.ws English Dictionary

rank-nullity theorem

rank-nullity theorem proper noun: 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).

Proper noun

the rank-nullity theorem

  1. 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.

Questions about rank-nullity theorem

What does rank-nullity theorem mean?
Rank-nullity theorem means 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).
What part of speech is rank-nullity theorem?
Rank-nullity theorem is a proper noun.

Words near rank-nullity theorem in the dictionary

  1. rank'd
  2. rank-and-file
  3. rank-and-filer
  4. rank-and-filers
  5. rank-deficient
  6. rank-nullity theorem
  7. rankability
  8. rankable
  9. rankachite
  10. rankamaite
  11. ranke

Source and license

Adapted from Wiktionary: rank-nullity theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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