Let X be a finite-dimensional normed linear space, and {x1; x2,..., xn} any basis for X. The function f: n X defined by is a

Let X be a finite-dimensional normed linear space, and {x1; x2,..., xn} any basis for X. The function f: „œn †’ X defined by

is a linear homeomorphism (remark 2.12). That is,
€¢ f is linear
€¢ f is one-to-one and onto
€¢ f and f-1 are continuous

F(21, 22, ..., ,) =4,x; i=1