Equation between Eq 167 and 168#9
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….lean Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
….lean Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Seems mathlib upgrade broke two things:
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eric-wieser
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May 28, 2023
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| lemma reindex_equiv_eq_if_matrix_eq (e₁ : m ≃ o) (e₂: n ≃ p) (A B: matrix m n R) : | ||
| (reindex e₁ e₂ A = reindex e₁ e₂ B) → A = B := | ||
| begin | ||
| intro h, | ||
| rw ← matrix.ext_iff at h, | ||
| funext r s, | ||
| specialize h (e₁ r) (e₂ s), | ||
| simp only [reindex_apply, submatrix_apply, equiv.symm_apply_apply] at h, | ||
| exact h, | ||
| end |
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This is (reindex e₁ e₂).injective
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| lemma reindex_equiv_eq_iff_matrix_eq (e₁ e₂ : n ≃ m) (A B: matrix n n R) : | ||
| (reindex e₁ e₂ A = reindex e₁ e₂ B) ↔ A = B := | ||
| ⟨ reindex_equiv_eq_if_matrix_eq _ _ _ _, matrix_eq_if_reindex_equiv _ _ _ _⟩ |
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Based on my comments below, I think this whole file can be discarded.
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I'll do a version bump separately |
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Rank One Update by Concatenation of inverse Equation
With$X$ an $(m+1)\times m$ matrix and $v$ a $(m+1)\times 1$ vector and $\alpha$ defined as:
$$\alpha = v^Tv - v^TXAX^Tv$$ $A$ $A=(X^TX)^{-1}$ we have:
and
In addition there are auxiliary lemmas:
reindex_equiv_eq_iff_matrix_eq (e₁ e₂ : n ≃ m) (A B: matrix n n R): two matrices A and B are equal if after re-indexing by an equivalent re-index set they are equal and vice versa.reindex_equiv_eq_if_matrix_eqandmatrix_eq_if_reindex_equiv: give the forward and reverse directions of the lemmas aboverank_one_update_transpose_mul_self: the rank one update by concatenation with a matrix when transposed and multiplied into itself can be expressed as aThis Pull Request starts from where PR #8 ends. The new changes in this PR are Equation between 167 and 168 and the lemmas mentioned above in two files
mat_vec_append.leanand `reindex.lean' in the 'for_mathlib' folder.