Theorems · Theorem · linear algebra

Matrix.det_mul_row

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (v : n → R)
  (A : Matrix n n R), (Matrix.of fun i j => v j * A i j).det = (∏ i, v i) * A.det

Multiplying each row by a fixed v i multiplies the determinant by the product of the vs.

Defined in

Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

DecidableEqFintypeCommRing