Linear Algebra

• Interesting applications of matrix multiplication. (e.g. path counting via adjacency matrices, Markov chains, exchange economies.)
• Geometry of linear transformations.
• Fitting data to equations. (Direct and via determinants.)
• Explore interesting matrix groups.
• Least squares and overdetermined systems.
• Behavior of algorithms (e.g. least squares) when they nearly fail.
• Traffic flows and linear equations.
• Codes obtained via matrix multiplication.
• Roundoff error in matrix operations.
• Convergence of power series in matrices.
• Computer assistance for Gram-Schmidt either geometrically or for orthogonal polynomials.
• Powers of matrices and eigenvalues.
• Difference equations.
• Geometry of diagonalizing quadratic forms.
• Interpretation of linear ODE solutions (e.g damped driven harmonic oscillators.)
• Web Resources:

  Mathlab:

  http://www.mathlab.cornell.edu/computer_and_portfolio/index.html#LINALG

  Connected Curriculum Project:

  
  http://www.math.duke.edu/education/ccp/materials/linalg/index.html

  Row Operations Applet:

  
  http://people.hofstra.edu/faculty/Stefan_Waner/tutorialsf1/javapiv.html

  Linear Transformation Applet:

  http://math.smith.edu/$\tilde{\ }$patela/Applets/transf_index.html

  Images of Transformations Applet:

  http://www.ies.co.jp/math/java/misc/lintra/lintra.html