Theorems · Theorem · linear algebra
LinearMap.index_smul
∀ {M : Type u_1} {N : Type u_2} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] {k : Type u_3} [inst_2 : Field k]
[inst_3 : Module k M] [inst_4 : Module k N] {f : M →ₗ[k] N} (t : k), t ≠ 0 → (t • f).index = f.index- Defined in
- Mathlib.Algebra.Module.LinearMap.Index
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- HasQuotient.Quotientproof · cited by 2,301
- Module.finrankproof · cited by 1,770
- LinearMap.rangeproof · cited by 893
- LinearMap.kerproof · cited by 848
- LinearMap.indexstatement and proof · cited by 11
- LinearMap.index_eq_finrank_subproof · cited by 8
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