Preface fo r Instructor s This book is intended t o provide an introduction to finite frames, pre - sented a t a leve l suitable fo r student s i n th e late r stage s o f their un - dergraduate studies . Thi s boo k evolve d fro m th e result s o f Deguan g Han an d Dav e Larso n i n [42] , which forme d th e kerne l fo r materia l about frame s presente d i n a n NSF-sponsore d RE U (Researc h Expe - rience for Undergraduates ) a t Texa s A&M University entitle d Matrix Analysis and Wavelets. Th e RE U wa s led by Dave Larson whil e Eri c Weber an d Ker i Kornelso n acte d a s mentors an d co-instructors . The REU students found frame s particularl y enticin g because th e questions can be approached usin g techniques from linea r algebra an d geometry. The y wer e excite d b y th e fac t tha t ther e ar e interestin g open question s regardin g frame s i n finite dimensions , an d eve n mor e enthusiastic onc e the y realize d tha t frame s hav e widesprea d applica - tions to a variety of mathematical, scientific , an d industrial problems . We wished to develop a resource which would help undergraduate stu - dents gai n acces s t o thi s burgeonin g are a o f mathematics . The stud y o f finite frame s provide s a n excellent , highl y motivat - ing framewor k (pardo n th e pun ) i n whic h t o introduc e th e essential s of matri x analysi s an d th e rudiment s o f finite-dimensional operato r theory. Student s lear n the mathematical theor y while simultaneousl y seeing how operator theor y i s used to develop a body of results abou t frames. Man y o f th e 5 0 o r s o student s wh o hav e participate d i n ix
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