Theorems · Theorem · linear algebra
Matrix.rank_diagonal
∀ {m : Type um} {R : Type uR} [inst : Field R] [inst_1 : Fintype m] [inst_2 : DecidableEq m] [inst_3 : DecidableEq R]
(w : m → R), (Matrix.diagonal w).rank = Fintype.card { i // w i ≠ 0 }The rank of a diagonal matrix is the count of non-zero elements on its main diagonal
- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- LinearMapproof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Cardinalproof · cited by 2,598
- Module.finrankproof · cited by 1,770
- Fintype.cardstatement and proof · cited by 1,386
- LinearMap.rangeproof · cited by 893
- Matrix.diagonalstatement and proof · cited by 314
- Cardinal.toNatproof · cited by 153
- Matrix.toLin'proof · cited by 86
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.rank_eq_rank_diagonalproof · cited by 1
- Matrix.exists_rank_normal_formproof · cited by 0
- Matrix.IsHermitian.rank_eq_card_non_zero_eigsproof · cited by 0