Theorems · Theorem · linear algebra
Matrix.linearIndependent_rows_of_isUnit
∀ {R : Type u_1} [inst : Semiring R] {m : Type u_3} [inst_1 : Fintype m] {A : Matrix m m R} [inst_2 : DecidableEq m],
IsUnit A → LinearIndependent R A.row- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringFintypeDecidableEq
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- IsUnitstatement and proof · cited by 1,602
- LinearIndependentstatement · cited by 560
- Matrix.rowstatement · cited by 40
- Matrix.vecMul_injective_iffproof · cited by 4
- Matrix.vecMul_injective_of_isUnitproof · cited by 2
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