Theorems · Theorem · linear algebra

Matrix.scalar_comm

∀ {m : Type u_2} {n : Type u_3} {α : Type u_11} [inst : Semiring α] [inst_1 : DecidableEq n] [inst_2 : Fintype n]
  [inst_3 : DecidableEq m] [inst_4 : Fintype m] (r : α),
  (∀ (r' : α), Commute r r') → ∀ (M : Matrix m n α), (Matrix.scalar m) r * M = M * (Matrix.scalar n) r

A version of Matrix.scalar_commute for rectangular matrices.

Defined in

Mathlib.Data.Matrix.Basic

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqFintypeDecidableEqFintype