Theorems · Theorem · linear algebra
Matrix.range_mulVecLin
∀ {R : Type u_1} [inst : CommSemiring R] {m : Type u_4} {n : Type u_5} [inst_1 : Fintype n] (M : Matrix m n R),
M.mulVecLin.range = Submodule.span R (Set.range M.col)- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapproof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- Submodule.spanstatement and proof · cited by 1,504
- LinearMap.rangestatement and proof · cited by 893
- Matrix.transposeproof · cited by 389
- Matrix.colstatement and proof · cited by 56
- Matrix.mulVecLinstatement · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.rank_eq_finrank_span_colsproof · cited by 3
- Matrix.range_toLin'proof · cited by 0