Theorems · Theorem · commutative algebra
spectralNorm_smul
∀ {K : Type u_2} [inst : NormedField K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] [IsUltrametricDist K]
(k : K) {y : L}, IsAlgebraic K y → spectralNorm K L (k • y) = ↑‖k‖₊ * spectralNorm K L yThe spectral norm is compatible with the action of K.
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- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites26
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- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- FiniteDimensionalproof · cited by 1,854
- NNReal.toRealstatement and proof · cited by 1,260
- NormedFieldstatement and proof · cited by 1,084
- IntermediateFieldproof · cited by 988
- NNNorm.nnnormstatement and proof · cited by 952
- IntermediateField.adjoinproof · cited by 382
- IsUltrametricDiststatement and proof · cited by 177
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