Theorems · Definition · linear algebra
Matrix.frobeniusNormedRing
{m : Type u_3} → {α : Type u_5} → [Fintype m] → [RCLike α] → [DecidableEq m] → NormedRing (Matrix m m α)Normed ring instance (using the Frobenius norm) for matrices over ℝ or ℂ. Not
declared as an instance because there are several natural choices for defining the norm of a
matrix.
- Defined in
- Mathlib.Analysis.Matrix.Normed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeRCLikeDecidableEq
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.
- Fintypestatement and proof · cited by 7,736
- Ringproof · cited by 7,463
- Matrixstatement and proof · cited by 4,303
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupproof · cited by 2,671
- NormedRingstatement · cited by 924
- Matrix.frobeniusSeminormedAddCommGroupproof · cited by 18
- Matrix.frobenius_norm_mulproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.frobeniusNormedAlgebrastatement · cited by 0