Theorems · Theorem · linear algebra
Matrix.Pivot.mul_listTransvecRow_last_col
∀ {𝕜 : Type u_3} [inst : Field 𝕜] {r : ℕ} (M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜) (i : Fin r ⊕ Unit),
(M * (Matrix.Pivot.listTransvecRow M).prod) i (Sum.inr ()) = M i (Sum.inr ())Multiplying by all the matrices in listTransvecRow M does not change the last column.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites5
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
- le_rflproof · cited by 1,558
- Matrix.Pivot.listTransvecRowstatement and proof · cited by 9
- Matrix.Pivot.mul_listTransvecRow_last_col_takeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_rowproof · cited by 1