Theorems · Theorem · linear algebra

Matrix.det_updateRow_sum

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (A : Matrix n n R)
  (j : n) (c : n → R), (A.updateRow j (∑ k, c k • A k)).det = c j • A.det

If we replace a row of a matrix by a linear combination of its rows, then the determinant is multiplied by the coefficient of that row.

Defined in

Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Cited by

3 results in Mathlib

Foundations

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

Assumes

DecidableEqFintypeCommRing