Theorems · Definition · functional analysis
Matrix.toEuclideanLin
{𝕜 : Type u_3} →
[inst : RCLike 𝕜] →
{m : Type u_7} →
{n : Type u_8} → [Fintype n] → [DecidableEq n] → Matrix m n 𝕜 ≃ₗ[𝕜] EuclideanSpace 𝕜 n →ₗ[𝕜] EuclideanSpace 𝕜 mA shorthand for Matrix.toLpLin 2 2.
- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- EuclideanSpacestatement · cited by 307
- Matrix.toLpLinproof · cited by 14
Cited by23
Results whose statement or proof uses this declaration.
- Matrix.isSymmetric_toEuclideanLin_iffstatement · cited by 3
- Matrix.toEuclideanLin_eq_toLin_orthonormalstatement · cited by 2
- Matrix.permMatrix_l2_opNorm_leproof · cited by 2
- Matrix.isPositive_toEuclideanLin_iffstatement and proof · cited by 2
- Matrix.l2_opNorm_defstatement · cited by 2
- Matrix.l2_opNorm_mulVecproof · cited by 2
- Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitaryproof · cited by 1
- InnerProductSpace.symm_toEuclideanLin_rankOnestatement · cited by 1
- LinearMap.posSemidef_toMatrix_iffproof · cited by 1
- Matrix.l2_opNorm_mulproof · cited by 1
- Matrix.toEuclideanLin_applystatement · cited by 0
- Matrix.toEuclideanLin_apply_piLp_toLpstatement · cited by 0