Theorems · Theorem · linear algebra
Matrix.Pivot.mul_listTransvecRow_last_col_take
∀ {𝕜 : Type u_3} [inst : Field 𝕜] {r : ℕ} (M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜) (i : Fin r ⊕ Unit) {k : ℕ},
k ≤ r → (M * (List.take k (Matrix.Pivot.listTransvecRow M)).prod) i (Sum.inr ()) = M i (Sum.inr ())Multiplying by some of the matrices in listTransvecRow M does not change the last column.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Matrixstatement and proof · cited by 4,303
- LT.lt.leproof · cited by 2,189
- Matrix.mul_oneproof · cited by 45
- Matrix.transvectionproof · cited by 24
- Matrix.Pivot.listTransvecRowstatement and proof · cited by 9
- Matrix.mul_transvection_apply_of_neproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.Pivot.mul_listTransvecRow_last_colproof · cited by 1
- Matrix.Pivot.mul_listTransvecRow_last_rowproof · cited by 1