Theorems · Theorem · linear algebra

Matrix.swap_mul_apply_left

∀ {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 : n) (a : m) (g : Matrix n m R), (Matrix.swap R i j * g) i a = g j a

Multiplying with swap R i j on the left swaps the i-th row with the j-th row.

Defined in

Mathlib.LinearAlgebra.Matrix.Swap

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqFintype