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Theorems · Theorem · linear algebra

Matrix.det_mul_comm

∀ {m : Type u_1} [inst : DecidableEq m] [inst_1 : Fintype m] {R : Type v} [inst_2 : CommRing R] (M N : Matrix m m R),
  (M * N).det = (N * M).det

On square matrices, mul_comm applies under det.

Defined in
Mathlib.LinearAlgebra.Matrix.Determinant.Basic
Cited by
3 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqFintypeCommRing
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Around this declaration

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Matrix.charpoly_mul_comm' · cited by 2Matrix.charpoly_mul_comm'Matrix.det_mul_right_comm · cited by 1Matrix.det_mul_right_commMatrix.det_mul_left_comm · cited by 0Matrix.det_mul_left_commCommRing · cited by 17173CommRingFintype · cited by 7736FintypeMatrix · cited by 4303Matrixmul_comm · cited by 2262mul_commMatrix.det · cited by 665Matrix.detMatrix.det_mul · cited by 51Matrix.det_mulMatrix.det_mul_commCITED BYCITES

Cites6

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Cited by3

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