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  Currently: Eigenspace
Upcoming: Bach and Tone, A Study of Voicemail

Eigenspace of a Matrix
Impressive... Looksmart.com hands me this when I search on eigenspace:
The eigenspace associated with the eigenvalue c of a matrix A is the null space of A - c*I.
Touchè, the rest of you lousy engines! An actual math courses' glossary of linear algebra terms. In simple terms for stupid people like me.

Thursday, October 7, 1999 - 12:30 p.m.

Flying Eigensignment
At least this one has a picture detailing the lateral-directional modal coupling relationships. And an arrow from that points to a cryptic graph.

Not quite enlightened as to what the goal of all the eigenspace is here?
This effort will provide design guidance on how to select closed-loop lateral-directional eigenvectors to achieve desired flying qualities. In addition, these guidelines will assist designers in performing trade-offs between flying qualities and other important design requirements, such as. achieving realizable gain magnitudes or desired system robustness.

Thursday, October 7, 1999 - 07:00 a.m.

Utilizing the fearful FrontPage Theme of Doom, Eigenmedia places their design emphasis on ease of use and swift download times. How nice! And though they sell a wide variety of services, from the Bible to Windows 95, their FAQ still doesn't explain why they chose to call their startup business Eigenmedia.

Wednesday, October 6, 1999 - 07:30 a.m.

From Kenneth B. Russell, Master of Perceptual Computing, comes the Eigenheads.
Modular eigenspaces are used to decorrelate eigenfeatures (eyes, nose, and mouth) from the rest of the head data. We observe that the modular eigenspace encoding often does not perform as well as a single eigenspace, and offer reasons for this based on experimental evidence.
Also see the conclusion, in which Master Russell seems to be a proponent of the "things gained instability and it all went wack" theory.

Tuesday, October 5, 1999 - 12:30 p.m.

First, an open challenge. Find eigenspace in a major online dictionary or encyclopedia. It's just not there.

So where do we learn what this mystical concept is all about? Try Js Ouyang, an AOLing math geek who thought it might be clever to name his page after a mathematical concept of "one's own space".
"The eigenvectors of A corresponding to an eigenvalue j are the nonzero vectors x that satisfy Ax = jx. Equivalently, the eigenvectors corresponding to j are the nonzero vectors in the solution of (jI - A)x = 0. We call this solution space the eigenspace of A corresponding to j."
Elementary linear algebra, apparently. What?

More mathymaticians sock it out over eigenspace, mainly trying to figure out why their eigenvectors are sticking out of their eigenvalues.

Eigen, eigen, eigen. Obviously a German prefix. So, I turn to Robert Beard's most excellent Web of On-line Dictionaries to find out that there are a lot of words that include "eigen" in them. And many of them do have to do with ownership.

Better still, the actual word eigen returns several meanings. But in addition to "own", "proper", "inherent", and "appropriate (to)", it also takes on the "peculiar" sense.

What could be so peculiar about eigenspace? A manifold of said substance can apparently be used in general purpose face recognition.

It's also a part of the most horrific acronym known to scholars, the Self-Organizing Hierarchical Optimal Subspace Learning and Inference Framework (SHOSLIF). Apparently here the eigenspace is used for a partition tree to separate faces and object characteristics for more magickal recognition.

By now, I know what you're thinking: How can I get some eigenspace going in my computer this very instant? Well good sir and/or madam, drop by the Vision Research Lab for a 10k zip file with source for using eigenspace in face recognition, video coding, pose estimation, and dishwashing. Okay, maybe not dishwashing. You best have an IRIX box sitting close at hand to compile from the included Makefile, but it's just C so it shan't be long until I have my own personal eigenspace to play in.

After all this, what exactly is eigenspace? It's a matrix simplification scheme that sounds too complex to comprehend. And lots of scary people in Utah use it.
h(p,q,d,i) = H^{p,q}(X_{d,n})(i), the z^i-eigenspace, where z = exp( 2pi i/d) and X_{d,n} is a d-sheeted cyclic branched cover.

Monday, October 4, 1999 - 11:00 p.m.

Instead of just syndicating per-day random content that varies by the link, I have decided to try switching it up with large, chunky updates that feed you information about obscure topics over longer periods of time.
It's a site that covers a wide range of diverse oddness.
I call it a "changing link list", or "stupid" for short.

Why this?
Struck by a bolt of blue by the etymology of the word "eigenspace" and associated eigencompounds in EFnet #pokey. Being half one language, and half another, a definition is hard to come by in the web of dictionaries. Learning follows.

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Dan Fitch dgfitch@yahoo.com
Thanks to the wonder-full folk of Pitas.com for hosting my old-fashioned link-list!