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Matrices, Geometry & Mathematica

This is not your parents' linear algebra course. The focus is on matrix action, the geometry of matrix action, and the underlying reasons for what we see, how we solve, and what makes it all work. The foundation is the singular value decomposition of matrices.

Here's the list of lessons.

	Perpendicular Frames		Ill-conditioned Matrices and Roundoff
	2D Matrix Action		Subspaces, Spans, Dimension, etc.
	Using Aligners, Stretchers and Hangers		Eigensense: Diagonalization, Exponential, etc.
	SVD Analysis of 2D Matrices		The Spectral Theorem for Symmetric Matrices
	3D Matrices		Function Spaces and RMS Approximation
	Beyond 3D

Here are some pages with snapshots of problems from the course. Be careful if you look at these. They are chock full of graphics, and may take very long to download.

• The singular value decomposition from the basics.
• Looking at reflections off mirrors from the tutorials.
• Visual evidence of linear independence from the problems.

If you want, you may download pre-evaluated samplers from this course.

If you have a Macintosh computer: Click and hold and save the file to your disk.

If you have a Windows machine: Right mouse click and save.

Here's a sampler from each lesson.

Lesson 1 Sampler Lesson 2 Sampler Lesson 3 Sampler Lesson 4 Sampler

Lesson 5 Sampler Lesson 6 Sampler Lesson 7 Sampler Lesson 8 Sampler

Lesson 9 Sampler Lesson 10 Sampler Lesson 11 Sampler

If you are new to the courseware's structure, or to the structure of Mathematica notebooks, take a quick look at what to do once you download a sample lesson.

To view the samples, if you don't have a copy of Mathematica, you'll need to download a copy of MathReader from Wolfram Research, Inc