Theorems · Theorem · linear algebra
Matrix.norm_le_iff
∀ {m : Type u_3} {n : Type u_4} {α : Type u_5} [inst : Fintype m] [inst_1 : Fintype n]
[inst_2 : SeminormedAddCommGroup α] {r : ℝ}, 0 ≤ r → ∀ {A : Matrix m n α}, ‖A‖ ≤ r ↔ ∀ (i : m) (j : n), ‖A i j‖ ≤ r- Defined in
- Mathlib.Analysis.Matrix.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement and proof · cited by 5,413
- Matrixstatement and proof · cited by 4,303
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- SeminormedAddGroupproof · cited by 331
- Matrix.seminormedAddCommGroupstatement · cited by 27
- pi_norm_le_iff_of_nonnegproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- Int.Matrix.exists_ne_zero_int_vec_norm_leproof · cited by 1