Theorems · Theorem · linear algebra
Matrix.frobenius_nnnorm_def
∀ {m : Type u_3} {n : Type u_4} {α : Type u_5} [inst : Fintype m] [inst_1 : Fintype n]
[inst_2 : SeminormedAddCommGroup α] (A : Matrix m n α), ‖A‖₊ = (∑ i, ∑ j, ‖A i j‖₊ ^ 2) ^ (1 / 2)- Defined in
- Mathlib.Analysis.Matrix.Normed
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- NNRealstatement · cited by 4,310
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Finset.sum_congrproof · cited by 2,323
- NNNorm.nnnormstatement and proof · cited by 952
- NNReal.sqrtproof · cited by 91
- Matrix.frobeniusSeminormedAddCommGroupstatement · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.frobenius_nnnorm_diagonalproof · cited by 2
- Matrix.frobenius_nnnorm_map_eqproof · cited by 2
- Matrix.frobenius_nnnorm_transposeproof · cited by 2
- Matrix.frobenius_norm_defproof · cited by 2
- Matrix.frobenius_nnnorm_mulproof · cited by 1