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Theorems · Theorem · linear algebra

Matrix.updateRow_ne

∀ {m : Type u_2} {n : Type u_3} {α : Type v} {M : Matrix m n α} {i : m} {b : n → α} [inst : DecidableEq m] {i' : m},
  i' ≠ i → M.updateRow i b i' = M i'
Defined in
Mathlib.LinearAlgebra.Matrix.RowCol
Cited by
16 results in Mathlib
Foundations
Depth 15 from the axioms · uses Quot.sound
Assumes
DecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Matrix.updateRow_apply · cited by 9Matrix.updateRow_applyMatrix.det_updateRow_add_smul_self · cited by 4Matrix.det_updateRow_add_…Matrix.updateRow_mul · cited by 2Matrix.updateRow_mulMatrix.submatrix_updateRow_succAbove · cited by 2Matrix.submatrix_updateRo…Matrix.cramer_transpose_row_self · cited by 2Matrix.cramer_transpose_r…Matrix.mul_adjp_apply_ne · cited by 2Matrix.mul_adjp_apply_nePolynomial.sylvesterDeriv_updateRow · cited by 1Polynomial.sylvesterDeriv…Polynomial.discr_of_degree_eq_two · cited by 1Polynomial.discr_of_degre…Matrix.updateRow_eq_transvection · cited by 1Matrix.updateRow_eq_trans…Matrix.det_eq_of_forall_row_eq_smul_add_const_aux · cited by 1Matrix.det_eq_of_forall_r…Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux · cited by 1Matrix.det_eq_of_forall_r…Matrix.update_vecMulVec · cited by 1Matrix.update_vecMulVecMatrix.det_updateRow_add_self · cited by 1Matrix.det_updateRow_add_…Matrix.det_updateRow_eq_zero · cited by 1Matrix.det_updateRow_eq_z…Matrix.det_vecMulVec · cited by 0Matrix.det_vecMulVecMatrix · cited by 4303MatrixFunction.update_of_ne · cited by 198Function.update_of_neMatrix.updateRow · cited by 63Matrix.updateRowMatrix.updateRow_neCITED BYCITES

Cites3

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

Cited by16

Results whose statement or proof uses this declaration.