Abstract: This paper shows how linear algebra can be done better without determinants. The standard proof that a square matrix of complex numbers has an eigenvalue uses determinants. The simpler and clearer proof presented here provides more insight and avoids determinants. Without using determinants, this allows us to define the multiplicity of an eigenvalue and to prove that the number of eigenvalues, counting multiplicities, equals the dimension of the underlying space. Without using determinants, we can define the characteristic and minimal polynomials and then prove that they behave as expected. This leads to an easy proof that every matrix is similar to a nice upper-triangular one. Turning to inner product spaces, and still without mentioning determinants, this paper gives a simple proof of the finite-dimensional spectral theorem.

This paper was published in the American Mathematical Monthly 102 (1995), 139-154.
In 1996 this paper received the Lester R. Ford Award for expository writing from the Mathematical Association of America.

Good explanation of black hole physics (in german).

The keyboard mapping can be modified via the registry on Windows 2000, XP (and presumably Vista, but the article is too old for Vista).

Interesting site, found via Wikipedia (Voronin's Zeta Universality Theorem)

Nice set of programming puzzles. From c.l.l.

Why several programming languages should be taught.

Some interesting papers.

How to use ZFS snapshots as backup mechanism.

Details about Leopards "Time Machine", which appears to be less sophisticated than Plan 9 venti.

Interesting information about Matlab and how it manages memory (copy-on-write). From MP.