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Theorems · Theorem · linear algebra

Matrix.det_fin_zero

∀ {R : Type v} [inst : CommRing R] {A : Matrix (Fin 0) (Fin 0) R}, A.det = 1

Determinant of 0x0 matrix

Defined in
Mathlib.LinearAlgebra.Matrix.Determinant.Basic
Cited by
5 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearMap.normDet_of_subsingleton · cited by 2LinearMap.normDet_of_subs…Matrix.derivative_det_one_add_X_smul_aux · cited by 1Matrix.derivative_det_one…Matrix.emptyRows_isTotallyUnimodular · cited by 1Matrix.emptyRows_isTotall…Matrix.IsTotallyUnimodular.fromRows_unitlike · cited by 1IsTotallyUnimodular.fromR…Polynomial.discr_C · cited by 0Polynomial.discr_CCommRing · cited by 17173CommRingMatrix · cited by 4303MatrixMatrix.det · cited by 665Matrix.detMatrix.det_isEmpty · cited by 9Matrix.det_isEmptyMatrix.det_fin_zeroCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.