Theorems · Definition · number theory
NumberField.basisMatrix
(K : Type u_1) → [inst : Field K] → [NumberField K] → Matrix (K →+* ℂ) (K →+* ℂ) ℂ
The basis matrix for the embeddings of K into ℂ. This matrix is formed by
taking the lattice basis vectors of K and reindexing them according to the
equivalence equivReindex, then transposing the resulting matrix.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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.
- DFunLike.coeproof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- Matrixstatement · cited by 4,303
- NumberFieldstatement and proof · cited by 653
- Matrix.ofproof · cited by 336
- NumberField.equivReindexproof · cited by 7
- NumberField.canonicalEmbedding.latticeBasisproof · cited by 7
Cited by9
Results whose statement or proof uses this declaration.
- NumberField.basisMatrix_eq_embeddingsMatrixReindexstatement · cited by 2
- NumberField.det_of_basisMatrix_non_zerostatement · cited by 1
- NumberField.sign_discrproof · cited by 1
- NumberField.discr_eq_basisMatrix_det_sqstatement and proof · cited by 1
- NumberField.inverse_basisMatrix_mulVec_eq_reprstatement · cited by 1
- NumberField.canonicalEmbedding_eq_basisMatrix_mulVecstatement and proof · cited by 1
- NumberField.conj_basisMatrixstatement · cited by 1
- NumberField.house.basis_repr_norm_le_const_mul_houseproof · cited by 0
- NumberField.basisMatrix.congr_simpstatement and proof · cited by 0