Theorems · Theorem · linear algebra

Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec

∀ {n : Type u_1} {𝕜 : Type u_3} [inst : Field 𝕜] [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n 𝕜),
  ∃ L L' D,
    M =
      (List.map Matrix.TransvectionStruct.toMatrix L).prod * Matrix.diagonal D *
        (List.map Matrix.TransvectionStruct.toMatrix L').prod

Any matrix can be written as the product of transvections, a diagonal matrix, and transvections.

Defined in

Mathlib.LinearAlgebra.Matrix.Transvection

Cited by

3 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldDecidableEqFintype