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This Java applet gives a single example of the calculation of a matrix inverse.

First Paragraph: There are various useful ways to write a matrix as the product of two or three other matrices that have special properties.

A lesser known application of the SVD.

First Paragraph: Every teacher of linear algebra should be familiar with the matrix singular value decomposition (or SVD).

Quick, readable discussion of polar decomposition, singular value decomposition, and pseudoinverses, with examples.

Introduces five series of matrices (with MATLAB code to generate them) and asks students to find out everything they can about them (determinant, eigenvalues, eigenvectors) and prove the results.

Exercises that approximate the cosine curve from $$–\pi/2$$ to $$\pi/2$$ with best-fitting parabolas satisfying varioius constraints.

Introduces the main concepts of computer graphics in 2 and 3 dimensions in under 7 pages, with exercises.

Exposition of the theory of (not necessarily orthogonal) projections. Discusses orthogonal complements, adjoints, and matrix representations. Mentions generalization to complex vector spaces.

Proves existence of matrix exponential and explains effective ways of calculating it. Under a page in length.