Theorems · Theorem · number theory

QuadraticForm.toMatrix_comp

∀ {R : Type u_3} {N : Type u_5} {P : Type u_6} {n : Type w} [inst : Fintype n] [inst_1 : DecidableEq n]
  [inst_2 : CommRing R] [inst_3 : Invertible 2] [inst_4 : AddCommGroup N] [inst_5 : Module R N] (b : Module.Basis n R N)
  {m : Type w} [inst_6 : DecidableEq m] [inst_7 : Fintype m] [inst_8 : AddCommGroup P] [inst_9 : Module R P]
  (b' : Module.Basis m R P) (Q : QuadraticForm R P) (f : N →ₗ[R] P),
  QuadraticForm.toMatrix b (QuadraticMap.comp Q f) =
    ((LinearMap.toMatrix b b') f).transpose * QuadraticForm.toMatrix b' Q * (LinearMap.toMatrix b b') f

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqCommRingInvertibleAddCommGroupModuleDecidableEqFintypeAddCommGroupModule