Theorems · Theorem · linear algebra

Matrix.det_updateCol_smul_left

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (M : Matrix n n R)
  (j : n) (s : R) (u : n → R), ((s • M).updateCol j u).det = s ^ (Fintype.card n - 1) * (M.updateCol j u).det

Defined in

Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommRing