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Theorems · Theorem · linear algebra

Matrix.single_eq_of_single_single

∀ {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) (a : α), Matrix.single i j a = Matrix.of (Pi.single i (Pi.single j a))

See also single_eq_updateRow_zero and single_eq_updateCol_zero.

Defined in
Mathlib.Data.Matrix.Basis
Cited by
6 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.stdBasis_eq_single · cited by 3Matrix.stdBasis_eq_singleMatrix.single_eq_updateRow_zero · cited by 2Matrix.single_eq_updateRo…Matrix.of_symm_single · cited by 1Matrix.of_symm_singleMatrix.updateRow_zero_mul_updateCol_zero · cited by 0Matrix.updateRow_zero_mul…Module.Basis.matrix_apply · cited by 0Basis.matrix_applyMatrix.vec_single · cited by 0Matrix.vec_singleDFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivMatrix · cited by 4303MatrixMatrix.ext · cited by 540Matrix.extPi.single · cited by 518Pi.singleMatrix.of · cited by 336Matrix.ofPi.single_eq_same · cited by 144Pi.single_eq_sameMatrix.single · cited by 129Matrix.singlePi.single_eq_of_ne' · cited by 33Pi.single_eq_of_ne'Matrix.single_eq_of_single_si…CITED BYCITES

Cites9

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

Cited by6

Results whose statement or proof uses this declaration.