MAT 150A Final: MAT150A_DAY15_Oct31_Lecture

• School: UC-Davis
• Department: Mathematics
• Course: MAT 150A
• Professor: José Simental Rodríguez

Document Summary

Then the following are equivalent: f is an isometry and f , f ( x ) f ( y ) = x y x , y rn. = a a = then a = b. 2 = 3 need to show f is linear. f ( x + y ) = f ( x ) + f ( y ), x , y rn f ( x ) = f ( x ), r. To show f ( x + y ) = f ( x ) + f ( y ) use the lemma with. = f ( x ) + f ( y ) So, we need to show f ( x + y ) f ( x + y ) = (f ( x ) + f ( y )) (f ( x + y )) = (f ( x ) + f ( y )) (f ( x ) + f ( y ))