Vector spaces.

Unreal Tournament 2004 rocks! ‘Specially the cool 2 DVD, headphones included, special edition that cost me a grand total of $10 :).

I was accepted by Carnegie Mellon University a couple days ago but forgot to send in an essential financial aid document :(. Oh well, not a huge deal. Vanderbilt sent me a financial aid offer and in addition to the full tuition scholarship, they threw in $4000 in need based grants??? Craziness. I think it comes down to about $6,000 a year if I wish to go there. Only 2 universities to go…

As for the title, a vector space V is a set that is closed under vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element is represented by a list of n real numbers, scalars are real numbers, addition is componentwise, and scalar multiplication is multiplication on each term separately.

For a general vector space, the scalars are members of a field F, in which case V is called a vector space over F.

Euclidean n-space (R^n) is called a real vector space, and C^n is called a complex vector space.

Getting this out of my profile, from Blade Runner:

Batty: I’ve seen things you people wouldn’t believe. Attack ships on fire off the shoulder of Orion. I watched C-beams glitter in the dark near the Tannhauser gate. All those moments will be lost in time, like tears in rain. Time to die.

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