[Merged by Bors] - feat(linear_algebra): determinant of vectors in a basis #3919
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Also renames `equiv_fun_basis` to `is_basis.equiv_fun` in order to use dot notation.
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Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
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Thanks @robertylewis! |
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src/linear_algebra/basic.lean
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| @@ -1709,6 +1709,9 @@ rfl | |||
| @[simp] theorem map_zero : e 0 = 0 := e.to_linear_map.map_zero | |||
| @[simp] theorem map_smul (c : R) (x : M) : e (c • x) = c • e x := e.map_smul' c x | |||
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| @[simp] lemma map_sum [fintype ι] (u : ι → M) : e (∑ i, u i) = ∑ i, e (u i) := | |||
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Shouldn't this rather be done more generally for sums over finsets?
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Thanks 🎉 bors merge |
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From the sphere eversion project, define the determinant of a family of vectors with respects to a basis. The main result is `is_basis.iff_det` asserting a family of vectors is a basis iff its determinant in some basis is invertible. Also renames `equiv_fun_basis` to `is_basis.equiv_fun` and `equiv_fun_basis_symm_apply` to `is_basis.equiv_fun_symm_apply`, in order to use dot notation. Co-authored-by: Anne Baanen t.baanen@vu.nl Co-authored-by: Rob Lewis <Rob.y.lewis@gmail.com> Co-authored-by: Rob Lewis <rob.y.lewis@gmail.com>
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From the sphere eversion project, define the determinant of a family of vectors with respects to a basis. The main result is `is_basis.iff_det` asserting a family of vectors is a basis iff its determinant in some basis is invertible. Also renames `equiv_fun_basis` to `is_basis.equiv_fun` and `equiv_fun_basis_symm_apply` to `is_basis.equiv_fun_symm_apply`, in order to use dot notation. Co-authored-by: Anne Baanen t.baanen@vu.nl Co-authored-by: Rob Lewis <Rob.y.lewis@gmail.com> Co-authored-by: Rob Lewis <rob.y.lewis@gmail.com>
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From the sphere eversion project, define the determinant of a family of vectors with respects to a basis.
The main result is
is_basis.iff_detasserting a family of vectors is a basis iff its determinant in some basis is invertible.Also renames
equiv_fun_basistois_basis.equiv_funandequiv_fun_basis_symm_applytois_basis.equiv_fun_symm_apply, in order to use dot notation.Co-authored-by: Anne Baanen t.baanen@vu.nl
Note that this file
linear_algebra.matrixis becoming a mess. We should probably move a few things and add headers, but I didn't want to do this and add content at the same time (and also I'm toolazybusy right now).