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Theorems · Theorem · linear algebra

Matrix.single_apply_of_ne

∀ {m : Type u_2} {n : Type u_3} {α : Type u_7} [inst : DecidableEq m] [inst_1 : DecidableEq n] [inst_2 : Zero α] (i : m)
  (j : n) (c : α) (i' : m) (j' : n), ¬(i = i' ∧ j = j') → Matrix.single i j c i' j' = 0
Defined in
Mathlib.Data.Matrix.Basis
Cited by
16 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
DecidableEqDecidableEqZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Matrix.mul_single_apply_of_ne · cited by 4Matrix.mul_single_apply_o…Matrix.single_apply_of_col_ne · cited by 2Matrix.single_apply_of_co…Matrix.single_apply_of_row_ne · cited by 2Matrix.single_apply_of_ro…Matrix.TransvectionStruct.toMatrix_sumInl · cited by 2TransvectionStruct.toMatr…Matrix.single_mul_apply_of_ne · cited by 2Matrix.single_mul_apply_o…Matrix.blockTriangular_single · cited by 2Matrix.blockTriangular_si…RingCon.matrix_apply_single · cited by 1RingCon.matrix_apply_sing…Matrix.updateRow_eq_transvection · cited by 1Matrix.updateRow_eq_trans…Ideal.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…toMatrix_dualTensorHom · cited by 1toMatrix_dualTensorHomMatrix.diag_single_same · cited by 1Matrix.diag_single_sameMatrix.commutator_diag2_transvection · cited by 1Matrix.commutator_diag2_t…Matrix.gram_single · cited by 0Matrix.gram_singleMatrix.single · cited by 129Matrix.singleMatrix.single_apply_of_neCITED BYCITES

Cites1

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Cited by16

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