Chapter 5Sec. 5.1Eigenvectors & Eigenvalues: ExampleThe basic concepts presented here -eigenvectorsandeigenvalues-are not just useful in mathematics (both pure and applied), forinstance, to study continuous dynamical systems. They alsoprovide critical information in engineering design, and they arisenaturally in such fields as physics and computer science.V. Yushutin, UHMATH 23313 / 17
Chapter 5Sec. 5.1BackgroundConsider a linear transformationT:Rn→Rn. We know thatthere exists a uniquen×nmatrixAsuch thatT(x) =Axfor allxinRn.We are interested in finding the vectors that just get scaled up bythe transformationT, i.e. vectors that do not change directionduring the transformation.