equal
deleted
inserted
replaced
345 by (simp add: bij_def orthogonal_transformation_inj orthogonal_transformation_surj) |
345 by (simp add: bij_def orthogonal_transformation_inj orthogonal_transformation_surj) |
346 |
346 |
347 lemma\<^marker>\<open>tag unimportant\<close> orthogonal_transformation_inv: |
347 lemma\<^marker>\<open>tag unimportant\<close> orthogonal_transformation_inv: |
348 "orthogonal_transformation f \<Longrightarrow> orthogonal_transformation (inv f)" |
348 "orthogonal_transformation f \<Longrightarrow> orthogonal_transformation (inv f)" |
349 for f :: "'a::euclidean_space \<Rightarrow> 'a::euclidean_space" |
349 for f :: "'a::euclidean_space \<Rightarrow> 'a::euclidean_space" |
350 by (metis (no_types, hide_lams) bijection.inv_right bijection_def inj_linear_imp_inv_linear orthogonal_transformation orthogonal_transformation_bij orthogonal_transformation_inj) |
350 by (metis (no_types, opaque_lifting) bijection.inv_right bijection_def inj_linear_imp_inv_linear orthogonal_transformation orthogonal_transformation_bij orthogonal_transformation_inj) |
351 |
351 |
352 lemma\<^marker>\<open>tag unimportant\<close> orthogonal_transformation_norm: |
352 lemma\<^marker>\<open>tag unimportant\<close> orthogonal_transformation_norm: |
353 "orthogonal_transformation f \<Longrightarrow> norm (f x) = norm x" |
353 "orthogonal_transformation f \<Longrightarrow> norm (f x) = norm x" |
354 by (metis orthogonal_transformation) |
354 by (metis orthogonal_transformation) |
355 |
355 |