Theorems · Theorem · linear algebra
Matrix.mul_swap_of_ne
∀ {R : Type u_1} {n : Type u_2} {m : Type u_3} [inst : Semiring R] [inst_1 : DecidableEq n] [inst_2 : Fintype n]
{i j b : n} {a : m}, b ≠ i → b ≠ j → ∀ (g : Matrix m n R), (g * Matrix.swap R i j) a b = g a b- Defined in
- Mathlib.LinearAlgebra.Matrix.Swap
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringDecidableEqFintype
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Equiv.swapproof · cited by 197
- Equiv.swap_apply_of_ne_of_neproof · cited by 39
- Matrix.swapstatement · cited by 19
- PEquiv.mul_toMatrix_toPEquivproof · cited by 2
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