Theorems · Theorem · linear algebra

Matrix.det_updateRow_eq_zero

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {M : Matrix n n R}
  {i j : n}, i ≠ j → (M.updateRow j (M i)).det = 0

If we repeat a row of a matrix, we get a matrix of determinant zero.

Defined in

Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommRing