## Mathematics 210## Linear Algebra |

* Chapter 5: Eigenvalues and Eigenvectors *

- Lay, Section 5.1, Eigenvectors and Eigenvalues (pdf)
- Lay, Section 5.2, The Characteristic Equation (pdf)
- Lay, Section 5.3, Diagonalization (pdf)
- Lay, Section 5.4, Eigenvectors and Linear Transformations (pdf)
- Lay, Section 5.5, Complex Eigenvalues (pdf)
- Lay, Section 5.6, Discrete Dynamical Systems (pdf)
- Lay, Section 5.7, Applications to Differential Equations (pdf)
- Lay, Section 5.8, Iterative Estimates for Eigenvalues (pdf)

*Lay, Section 5.1, pp 308--310 --*5, 7, 9, 15, 17, 19, 25, 27 (eigenvalues of A^{-1}and A^{T}), 28, 29 (row sums), 33, 34 (discrete dynamical systems), 37, 39 (eigenspaces)*Lay, Section 5.2, pp 317--319 --*5, 11, 17, 18, 19, 23 (QR algorithm), 25, 27 (discrete dynamical systems), 30 (parameterized characteristic polynomials)*Lay, Section 5.3, pp 325--327 --*1, 5, 9, 15, 29 (non-unique matrix factorization), 31,32, 33, 35 (diagonalize matrices)*Lay, Section 5.4, pp 333--335 --*1, 3, 5, 7, 9, 11, 13, 15, 17, 25 (trace), 30, 32 (diagonalize a matrix)*Lay, Section 5.5, pp 341--342 --*3, 9, 15, 19, 23, 24 (eigenvalues of a symmetric matrix), 25, 26 (the rotation hidden within), 27 (block-diagonal matrix)*Lay, Section 5.6, pp 352--353 --*1, 3 (spotted owls and wood rats), 5, 6 (spotted owls and flying squirrels), 7 (graphing trajectories), 11, 16 (rental cars), 18 (buffalo herd)*Lay, Section 5.7, pp 361--362 --*1, 5, 7, 13, 17 (dynamical systems), 22 (RCL circuit)*Lay, Section 5.8, pp 368--370 --*1, 5, 9, 11 (Rayleigh quotient), 18 (inverse power method), 19 (approximate eigenvectors), 21 (strictly dominant eigenvalue)

Download the supporting pdf files and Mathematica notebooks from the Lay Linear Algebra web site.

*Dynamical Systems and Spotted Owls*- Photo of a Spotted Owl

The descriptions of the following projects, and their supporting Mathematica notebooks, are available from David Smith's Connected Curriculum Project at Duke University.

A study group hosted by the Institute for Advanced Study at Princeton offers some thoughts on teaching linear algebra. Their report includes the following project on the biology of loggerhead sea turtles which extends David Smith's treatment of Leslie matrices. Here is a supporting Mathematica notebook in three formats: nb pdf html.

*Loggerhead Sea Turtles**Photos of sea turtles*