Theorems · Theorem · commutative algebra

PowerBasis.leftMulMatrix

∀ {S : Type u_2} [inst : Ring S] {A : Type u_4} [inst_1 : CommRing A] [inst_2 : Algebra A S] (pb : PowerBasis A S),
  (Algebra.leftMulMatrix pb.basis) pb.gen =
    Matrix.of fun i j => if ↑j + 1 = pb.dim then -pb.minpolyGen.coeff ↑i else if ↑i = ↑j + 1 then 1 else 0

Defined in

Mathlib.RingTheory.PowerBasis

Cited by

0 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingCommRingAlgebra