Theorems · Theorem · linear algebra
Matrix.charpoly_mul_comm
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (A B : Matrix n n R),
(A * B).charpoly = (B * A).charpolyA version of charpoly_mul_comm' for square matrices.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Fintype.cardproof · cited by 1,386
- Matrix.charpolystatement · cited by 82
- IsRegular.leftproof · cited by 39
- Polynomial.isRegular_X_powproof · cited by 3
- Matrix.charpoly_mul_comm'proof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_toMatrixproof · cited by 9
- Matrix.IsHermitian.charpoly_eqproof · cited by 2
- Matrix.charpoly_units_conjproof · cited by 2
- Matrix.IsHermitian.charpoly_cfc_eqproof · cited by 0