ST259 Lecture : 2.5 - The Change of Coordinate Matrix
Document Summary
Weassume that v and w arefinite dimensionalvectorspacesover f. Let b and b betwo ordered basesfor a finite dimensional vectorspace v and let. Thematrix q ivis defined aboveis called a changeofcoordinatematrix becauseof abovethe we saythatq changesb coordinates intob coordinates observethatif. Noticethat if q changes b coordinatesintob coordinates then q changes b coordinates intob coordinates. Consider lineartransformationsthatmap avector space transformation is called a linearoperator on v suppose now that t is a linearoperator andthatbandb are orderedbasesfor v then t can on afinite dimensionalvectorspace be representedbythe matrices it bandi113 ontoitself such a linear. Thate t t be a linearoperator on a finite dimensional vectorspace v and let b and. B beordered basesfor v supposethat q is thechange ofcoordinatematrixthatchanges. Corollarmet acmmm f and let r be an ordered basisfor fn then la r q aq where. Q isthe mxn matrix whose j th column is the j th vectorof r.
