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).

“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.”

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

proper nounthe rank-nullity theorem
  1. linear algebraA 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.

Cite this entry
APA

rank-nullity theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/rank-nullity%20theorem

MLA

“rank-nullity theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/rank-nullity%20theorem. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “rank-nullity theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/rank-nullity%20theorem.

Source: rank-nullity theorem on Wiktionary, CC BY-SA 4.0.