Mathlib Map

Theorems · Definition · linear algebra

Matrix.cRank

{m : Type um} → {n : Type un} → {R : Type uR} → [Semiring R] → Matrix m n R → Cardinal.{max uR um}

The rank of a matrix, defined as the dimension of its column space, as a cardinal.

Defined in
Mathlib.LinearAlgebra.Matrix.Rank
Cited by
16 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.eRank · cited by 11Matrix.eRankMatrix.lift_cRank_submatrix · cited by 3Matrix.lift_cRank_submatr…Matrix.lift_cRank_submatrix_le · cited by 3Matrix.lift_cRank_submatr…Matrix.cRank_diagonal · cited by 1Matrix.cRank_diagonalMatrix.cRank_le_card_height · cited by 1Matrix.cRank_le_card_heig…Matrix.cRank_le_card_width · cited by 1Matrix.cRank_le_card_widthMatrix.cRank_one · cited by 1Matrix.cRank_oneMatrix.cRank_submatrix · cited by 1Matrix.cRank_submatrixMatrix.cRank_subsingleton · cited by 1Matrix.cRank_subsingletonMatrix.cRank_toNat_eq_finrank · cited by 1Matrix.cRank_toNat_eq_fin…Matrix.cRank_zero · cited by 1Matrix.cRank_zeroMatrix.eRank_toNat_eq_finrank · cited by 1Matrix.eRank_toNat_eq_fin…Matrix.cRank_reindex · cited by 0Matrix.cRank_reindexMatrix.cRank_submatrix_le · cited by 0Matrix.cRank_submatrix_leMatrix.cRank_toNat_eq_rank · cited by 0Matrix.cRank_toNat_eq_rankSemiring · cited by 13802SemiringSet.range · cited by 4705Set.rangeMatrix · cited by 4303MatrixCardinal · cited by 2598CardinalSubmodule.span · cited by 1504Submodule.spanModule.rank · cited by 496Module.rankMatrix.col · cited by 56Matrix.colMatrix.cRankCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by17

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