EE263Prof. S. BoydEE263 homework 1 additional exercise1.Affine functions.A functionf:Rn→Rmis calledaffineif for anyx, y∈Rnandanyα,β∈Rwithα+β= 1, we havef(αx+βy) =αf(x) +βf(y).(Without the restrictionα+β= 1, this would be the definition of linearity.)(a) Suppose thatA∈Rm×nandb∈Rm. Show that the functionf(x) =Ax+bisaffine.(b) Now the converse: Show that any affine functionfcan be represented asf(x) =Ax+b, for someA∈Rm×nandb∈Rm. (This representation is unique: for agiven affine functionfthere is only one
This is the end of the preview.
access the rest of the document.