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Theorems · Theorem · linear algebra

Matrix.one_apply_ne

∀ {n : Type u_3} {α : Type v} [inst : DecidableEq n] [inst_1 : Zero α] [inst_2 : One α] {i j : n}, i ≠ j → 1 i j = 0
Defined in
Mathlib.Data.Matrix.Diagonal
Cited by
39 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
DecidableEqZeroOne
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

RootPairing.GeckConstruction.ω_mul_ω · cited by 5GeckConstruction.ω_mul_ωUpperHalfPlane.denom_one · cited by 3UpperHalfPlane.denom_oneMatrix.fromBlocks_one · cited by 3Matrix.fromBlocks_oneMatrix.matPolyEquiv_charmatrix · cited by 3Matrix.matPolyEquiv_charm…EisensteinSeries.D2_one · cited by 2EisensteinSeries.D2_oneMatrix.Nonsingular.linearIndependent_col · cited by 2Nonsingular.linearIndepen…Matrix.TransvectionStruct.toMatrix_sumInl · cited by 2TransvectionStruct.toMatr…Matrix.toMvPolynomial_one · cited by 1Matrix.toMvPolynomial_oneIdeal.single_mem_jacobson_matrix · cited by 1Ideal.single_mem_jacobson…Matrix.diag2_decompose · cited by 1Matrix.diag2_decomposeMatrix.transvection_mem_commutator₁ · cited by 1Matrix.transvection_mem_c…Matrix.isDiag_one · cited by 1Matrix.isDiag_oneMatrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigen · cited by 1Matrix.lt_two_mul_of_mul_…Matrix.mul_adjp_add_detp · cited by 1Matrix.mul_adjp_add_detpMatrix.commutator_diag2_transvection · cited by 1Matrix.commutator_diag2_t…Matrix · cited by 4303MatrixMatrix.diagonal_apply_ne · cited by 50Matrix.diagonal_apply_neMatrix.one_apply_neCITED BYCITES

Cites2

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

Cited by39

Results whose statement or proof uses this declaration.