Theorems · Theorem · linear algebra
Matrix.nonsingular_mul_iff
∀ {R : Type u_1} {n : Type u_3} [inst : CommSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n] [IsCancelAdd R]
{A B : Matrix n n R}, (A * B).Nonsingular ↔ A.Nonsingular ∧ B.Nonsingular- Defined in
- Mathlib.LinearAlgebra.Matrix.Nonsingular
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- IsCancelAddstatement and proof · cited by 79
- Matrix.Nonsingularstatement and proof · cited by 27
- IsRightRegular.of_mulproof · cited by 7
- IsLeftRegular.of_mulproof · cited by 5
- Matrix.isLeftRegular_iff_nonsingularproof · cited by 3
- Matrix.isRightRegular_iff_nonsingularproof · cited by 2
- Matrix.Nonsingular.mulproof · cited by 1
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