2.4. Normed Space A norm on a (real or complex) vector space X is a real-valued function on at an x E X is denoted by ||x|| (read "norm of x") and which has the pro (NI) ||x|| > 0 (N2) ||x|| = 0 + x =...

Example solution
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="" on="" remark="" .="" the="" normed="" space="" just="" defined="" is="" denoted="" by="" (x,="" ||.="" ||="" )="" or="" simply="" examples="" 1)="" x="R" with="" the="" norm="" ||x||="|x|" x="" e="" r="" is="" normed="" space="" "/="">
Extracted text: 2.4. Normed Space A norm on a (real or complex) vector space X is a real-valued function on at 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="" on="" remark="" .="" the="" normed="" space="" just="" defined="" is="" denoted="" by="" (x,="" ||.="" ||="" )="" or="" simply="" examples="" 1)="" x="R" with="" the="" norm="" ||x||="|x|" x="" e="" r="" is="" normed="">