Example solution 2.4. Normed SpaceA norm on a (real or complex) vector space X is a real-valued function onat an x E X is denoted by ||x|| (read "norm of x") and which has the pro(NI) ||x|| > 0(N2) ||x|| = 0 + x = 0,(N3) || Ax|| = |2|||x||(N4) ||x + y|| < ||x|| + |ly|| Vx,y € X (Triangle inequality).V x E X,(Vx E X ,V 1 e K),Definition. A normed space is a vector space X with a norm defined onRemark . The normed space just defined is denoted by (X, ||. || ) or simplyExamples1) X = R with the norm ||x|| = |x| x E R is normed space

Name: Example solution 2.4. Normed SpaceA norm on a (real or complex) vector
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: Example solution 2.4. Normed SpaceA norm on a (real or complex) vector space X is a real-valued function onat an x E X is denoted by ||x|| (read "norm of x") and which has the pro(NI) ||x|| > 0(N2) ||x|| = 0 + x = 0,(N3) || Ax|| = |2|||x||(N4) ||x +