src/HOL/Multivariate_Analysis/Linear_Algebra.thy
changeset 62343 24106dc44def
parent 61973 0c7e865fa7cb
child 62397 5ae24f33d343
equal deleted inserted replaced
62342:1cf129590be8 62343:24106dc44def
  2750   by blast
  2750   by blast
  2751 
  2751 
  2752 lemma infnorm_Max:
  2752 lemma infnorm_Max:
  2753   fixes x :: "'a::euclidean_space"
  2753   fixes x :: "'a::euclidean_space"
  2754   shows "infnorm x = Max ((\<lambda>i. \<bar>x \<bullet> i\<bar>) ` Basis)"
  2754   shows "infnorm x = Max ((\<lambda>i. \<bar>x \<bullet> i\<bar>) ` Basis)"
  2755   by (simp add: infnorm_def infnorm_set_image cSup_eq_Max del: Sup_image_eq)
  2755   by (simp add: infnorm_def infnorm_set_image cSup_eq_Max)
  2756 
  2756 
  2757 lemma infnorm_set_lemma:
  2757 lemma infnorm_set_lemma:
  2758   fixes x :: "'a::euclidean_space"
  2758   fixes x :: "'a::euclidean_space"
  2759   shows "finite {\<bar>x \<bullet> i\<bar> |i. i \<in> Basis}"
  2759   shows "finite {\<bar>x \<bullet> i\<bar> |i. i \<in> Basis}"
  2760     and "{\<bar>x \<bullet> i\<bar> |i. i \<in> Basis} \<noteq> {}"
  2760     and "{\<bar>x \<bullet> i\<bar> |i. i \<in> Basis} \<noteq> {}"