src/HOL/Analysis/Linear_Algebra.thy
changeset 73932 fd21b4a93043
parent 73795 8893e0ed263a
child 73933 fa92bc604c59
equal deleted inserted replaced
73866:66bff50bc5f1 73932:fd21b4a93043
   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