Theorems · Theorem · linear algebra

Matrix.det_one_add_replicateCol_mul_replicateRow

∀ {m : Type u_2} {α : Type u_4} [inst : Fintype m] [inst_1 : DecidableEq m] [inst_2 : CommRing α] {ι : Type u_5}
  [inst_3 : Unique ι] (u v : m → α), (1 + Matrix.replicateCol ι u * Matrix.replicateRow ι v).det = 1 + v ⬝ᵥ u

A special case of the Matrix determinant lemma for when A = I.

Defined in

Mathlib.LinearAlgebra.Matrix.SchurComplement

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingUnique