HIRE QUALIFIED ACADEMIC WRITERS
Definition. Suppose that V and W are vector spaces over F. By a linear transformation from V to W,we mean a mapping T : V ? W satisfying the following conditions:(LT1) For every x, y ? V , we have T(x + y) = T(x) + T(y).(LT2) For every c ? F and x ? V , we have T(cx) = cT(x).Definition. Suppose that V is a vector space over F. A linear transformation T : V ? V is called alinear operator on V .Remark. Note that in the special case when W = F, a linear transformation T : V ? F is simply alinear functional on V .Definition. Suppose that V and W are normed vector spaces over F. Then a linear transformationT : V ? W is said to be bounded if there exists a real number M = 0 such that kT(x)k = Mkxk forevery x ? V . Attachments: lfa07.pdf
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