Theorems · Theorem · linear algebra
Matrix.rank_subsingleton
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : CommSemiring R] [Subsingleton R]
(A : Matrix m n R), A.rank = 1- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Matrix.rankstatement · cited by 48
- Module.finrank_subsingletonproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.rank_mul_le_leftproof · cited by 5
- Matrix.rank_mul_le_rightproof · cited by 2
- Matrix.rank_mul_eq_left_of_det_mem_nonZeroDivisorsproof · cited by 2
- Matrix.rank_submatrix_leproof · cited by 1
- Matrix.rank_vecMulVec_leproof · cited by 0