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Theorems · Theorem · linear algebra

Matrix.updateCol_apply

∀ {m : Type u_2} {n : Type u_3} {α : Type v} {M : Matrix m n α} {i : m} {j : n} {c : m → α} [inst : DecidableEq n]
  {j' : n}, M.updateCol j c i j' = if j' = j then c i else M i j'
Defined in
Mathlib.LinearAlgebra.Matrix.RowCol
Cited by
8 results in Mathlib
Foundations
Depth 16 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_transpose · cited by 12Matrix.updateRow_transposeMatrix.updateCol_transpose · cited by 5Matrix.updateCol_transposePolynomial.resultant_C_mul_right · cited by 5Polynomial.resultant_C_mu…Matrix.adjugate_transpose · cited by 5Matrix.adjugate_transposeAlgebra.discr_mul_isIntegral_mem_adjoin · cited by 1Algebra.discr_mul_isInteg…Matrix.map_updateCol · cited by 1Matrix.map_updateColisIntegral_discr_mul_of_mem_traceDual · cited by 0isIntegral_discr_mul_of_m…Module.Basis.toMatrix_update · cited by 0Basis.toMatrix_updateMatrix · cited by 4303MatrixMatrix.updateCol · cited by 45Matrix.updateColMatrix.updateCol_ne · cited by 11Matrix.updateCol_neMatrix.updateCol_self · cited by 11Matrix.updateCol_selfMatrix.updateCol_applyCITED BYCITES

Cites4

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Cited by8

Results whose statement or proof uses this declaration.