Ideas and Resources by
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.
Geometry of diagonalizing quadratic forms.
Interpretation of linear ODE solutions (e.g damped driven harmonic oscillators.)
Connected Curriculum Project:
Row Operations Applet:
Linear Transformation Applet:
Images of Transformations Applet: