The set of all linear transformations from a vector space V to a vector space W is denoted by L(V, W). If S and T are in L(V, W), we can define the sum S + T of S andT by (S+ T)(v) = S(v) + T(v) for all v in V. If c is a scalar, we define the scalar multiple cT of T byc to be (cT)(v) = cT(v) %3D for all v in V. Then S+ T and cTare both transformations from V to W.

The set of all linear transformations from a vector space V to a vector space W is denoted by L(V, W). If S and T are in L(V, W), we can define the sum S + T of S andT by (S+ T)(v) = S(v) + T(v) for all v in V. If c is a scalar, we define the scalar multiple cT of T byc to be (cT)(v) = cT(v) %3D for all v in V. Then S+ T and cTare both transformations from V to W.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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