day25.pdf - Chapter 5 MATH 2331 20947 Vladimir Yushutin [email protected] Office PGH 606 Lecture MoWeFr 10:00AM-11:00AM in CBB 104 Office hours Fr

day25.pdf - Chapter 5 MATH 2331 20947 Vladimir Yushutin...

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Chapter 5 MATH 2331 - 20947 Vladimir Yushutin [email protected] Office : PGH 606 Lecture : MoWeFr 10:00AM-11:00AM in CBB 104 Office hours : Fr 3:00PM-4:00PM and BY APPOINTMENT V. Yushutin, UH MATH 2331 1 / 17
Chapter 5 Sec. 5.1 Eigenvectors & Eigenvalues Section 5.1 V. Yushutin, UH MATH 2331 2 / 17
Chapter 5 Sec. 5.1 Eigenvectors & Eigenvalues: Example The basic concepts presented here - eigenvectors and eigenvalues - are not just useful in mathematics (both pure and applied), for instance, to study continuous dynamical systems. They also provide critical information in engineering design, and they arise naturally in such fields as physics and computer science. V. Yushutin, UH MATH 2331 3 / 17
Chapter 5 Sec. 5.1 Background Consider a linear transformation T : R n R n . We know that there exists a unique n × n matrix A such that T ( x ) = A x for all x in R n . We are interested in finding the vectors that just get scaled up by the transformation T , i.e. vectors that do not change direction during the transformation.

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