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Theorems · Theorem · linear algebra

Matrix.det_eq_one_of_card_eq_zero

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {A : Matrix n n R},
  Fintype.card n = 0 → A.det = 1
Defined in
Mathlib.LinearAlgebra.Matrix.Determinant.Basic
Cited by
2 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqFintypeCommRing
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Matrix.charpoly_monic · cited by 9Matrix.charpoly_monicMatrix.charpoly_degree_eq_dim · cited by 4Matrix.charpoly_degree_eq…CommRing · cited by 17173CommRingFintype · cited by 7736FintypeMatrix · cited by 4303MatrixFintype.card · cited by 1386Fintype.cardMatrix.det · cited by 665Matrix.detMatrix.det_isEmpty · cited by 9Matrix.det_isEmptyMatrix.det_eq_one_of_card_eq_…CITED BYCITES

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Cited by2

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