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Theorems · Theorem · linear algebra

Matrix.Nonsingular.mul

∀ {R : Type u_1} {n : Type u_3} [inst : CommSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {A : Matrix n n R}
  [IsCancelAdd R] {B : Matrix n n R}, A.Nonsingular → B.Nonsingular → (A * B).Nonsingular
Defined in
Mathlib.LinearAlgebra.Matrix.Nonsingular
Cited by
1 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringFintypeDecidableEqIsCancelAdd
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Around this declaration

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Matrix.nonsingular_mul_iff · cited by 0Matrix.nonsingular_mul_iffCommSemiring · cited by 10911CommSemiringFintype · cited by 7736FintypeMatrix · cited by 4303MatrixIsCancelAdd · cited by 79IsCancelAddMatrix.Nonsingular · cited by 27Matrix.NonsingularIsLeftRegular.mul · cited by 5IsLeftRegular.mulMatrix.isLeftRegular_iff_nonsingular · cited by 3Matrix.isLeftRegular_iff_…Nonsingular.mulCITED BYCITES

Cites7

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Cited by1

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