Two Birds With One Very Linear Stick

Here is the problem: whenever I have about more work than I can handle reasonably (or when I think I do), I want to procrastinate. Aside from RSS and Gaia and about a bunch of other things blogging is the next one.

But! I can make this productive! I have a linear algebra quiz in about two and a half hours, and I can take notes here while I blog (and/or mindlessly type).

This is inspired by Yuma's rather nonfunctional blog now, and I would link, but it contains his real name and mine, which would make all of these nicknames rather silly and pointless.

Anyway.

Determinants and eigenvalues. The chapter where I actually learned new things.

• The most generic way of finding the determinant of a matrix is to take one row/column and add all the (entry * cofactor of entry) for that row/column.
• Cofactor = (-1)^(row# + column# of entry) det (matrix without entry's row and column)
• This technically works with 2 x 2 matrices, but what you're essentially doing is ad - cb anyway.
• This process is officially called the cofactor expansion. I always think of it as the "reduce the matrix the determinant way."
• SPECIAL CASES:
• if one row/column is all 0, then obviously expand along that row/column = det(matrix) = 0
• if the matrix is an upper/lower triangular matrix, multiply entries along diagonal (this one's easy to see)
• det(k*matrix) = k^n * det(matrix)
• det(transpose of matrix) = det(matrix) since rows/columns preserve
• det(matrix A * matrix B) = det(A) * det(B); and the extrapolation of det(matrix^k) = det(matrix)^k
• Row operations & determinants:
• 1. interchanging = -det(matrix)
• 2. multiplying one row by k = k det(matrix)
• 3. adding mults of one row to another = det(matrix)
• 1 because of signs of cofactors; 2 because of factoring; 3 because of same entries in two rows
• If det(A) = 0, no inverse (gasp!) and otherwise, yes inverse where det(A^-1) = 1/det(A) (sort of like the "inverse" of a number).
• Matrices can be blocked off to make calculations easier (if applicable). Only helps if you can make a square block of 0s.
• Adjoint of a matrix is the transpose of the cofactors matrix (matrix with cofactor of each entry in place of the corresponding entry).
• For matrix A: A * adj(A) = det(A) * I = adj(A) * A and adj(A) / det(A) = A^-1, where the proof of the second comes from the dividing everything by det(A).
• det(adj(A)) = detA^(n-1) where A is n x n; derived from above formula
• Cramer's Rule: so confusing to write... (to find nth x, replace nth column with constant column in coefficient matrix then find det (that) / det(A)) however it's more difficult to calculate for larger matrices and therefore only useful in theory
• Diagonalization is useful for calculating powers of square matrices (that can be diagonalized).
• If a square matrix can be diagonalized, then P^-1 * A * P = D, where P is an invertible "diagonalizing" matrix (so many terms) and D is the "diagonalized" matrix.
• P = eigenvectors of A and D = eigenvalues of A, in respective order (eigenvalue 1 matches with eigenvector 1 in column location).
• Eigenvalues: AX = xX where x is a constant (the eigenvalue) that is usually lambda but I can't type it easily.
• Generally, eigenvalues are found by solving the characteristic polynomial, which is det(xI - A) = 0.
• The eigenvectors are found by solving for X when the eigenvalues are plugged in for (xI - A) * X = 0.
• side note: tr(A) is the trace of A and is the sum of all diagonal entries
• For P to exist, # of eigenvectors = # of columns in A (or the total multiplicity of the eigenvalues, or the # of rows in P)
• Similar matrices are similar (no pun intended) to A and D pairs, but the other matrix need not be D.
• if A ~ B (~ = is similar to):  A^-1, A^T, A^k ~ B^-1, B^T, B^k for k >= 0 respectively
• if A ~ B: det(A), c(x) of A, and eigenvalues of A = those of B; by this the matrix A has similar properties to the eigenvalues of A, e.g. if x^2 (the eigenvalue of A) = 5x, then A^2 = 5A.
• if A ~ B and B ~ C then A ~ C

 The rest is just stuff from before.

My other work consists of writing the two paragraphs I have blocked out for my paper today (I have the topic sentences and the research, so that should be easy), as well as another location-specific paragraph that I need to do a bit more research on that hopefully won't take too long, and hopefully I can tackle another part of my paper (bring it to three full pages) as well.

Then I have reviewing for my Java midterm, so I need to start on my assignment as well, since it's been said that having that done before the midterm is good review.

My mom suggested I listen to French radio, so I could do that in my spare time. I also need to start researching for Robot On Moon (hey, ROM is also Royal Ontario Museum!), and sign up for a project for FSAE, and talk with the person in charge of notes, and review at least calc and hopefully physics too, and finish my letter and send out the food, and write my story, and fit in all my Halloween parties, and figure out my linear algebra assignment eventually, and stop typing "assignmnet" every time I mean "assignment" because terminal doesn't recognize it and spits at me every time I do so.

But. First. Fooooood.

The Past Few Weeks

I have been going to my classes every other class. Sometimes it is intentional, like today, when I skipped my linear algebra class to attend a soldering tutorial that was probably more informative and productive than any single lecture I have gone to for linalg. (I stripped wires and made pretty twists with them and soldered them together with decent speed! That has to be one of the more productive hours I have ever spent in a long time).

Other times it is accidental, like today (again), when I woke up in the morning and it was 9:45 and my java class started at 9:35, and I was groggy and on the top bunk without any proper outdoors clothes on or any breakfast in my stomach, and the earliest I can have all of that done would be by 10, and then 5-10 minutes of walking to class would leave me with 15 minutes of lecture time left. So I promptly fell back asleep.

I asked Jessica later on about what the prof talked about in class today, and she said, "Calling a private property in another class with a public method." Which is, well, what we learned on Monday. I even have rather nice notes for that day.

I think it was on Monday, too, that I left my java class and, after buying yogurt and granola for breakfast, hurried to my linalg class and read the part in the textbook where I thought we had gone over the class before. And I went into class an hour later and proceeded to hear about the same things I had just read.

As Yuma puts it, "Why are your classes so useless?"

I like to believe that it is only so because I am in this limbo mode right now where I can't actually take the exciting classes. But I do have some neat classes next semester, like intro to computer engineering and engineering economy, as well as differential equations which I've heard is actually tough (or maybe they are making it up just like they are making up how difficult linear algebra was going to be). Also I will have no more English classes next semester and, as long as my 93% fixed schedule (based on rough approximations) is not changed by the higher beings who design the electrical engineering curriculum here, I will never have an official English class again.

Or maybe they do this English thing at grad school too. Who knows. I think they should do it every year but I suppose the workload (essay-writing) does add up.

. . .

I found a couple of tunnels under my school. This would sound so much cooler if I also put in, "I sneaked past -insert integer here- security guards and ducked under the camera and picked the lock on the grate and lowered myself into the tunnels," but alas, that was not the case. These tunnels are university-sanctioned, opened for the special purpose of allowing us to get to our classes without freezing ourselves to death when it is -40 degrees Celsius outside and the snow is piled higher than your head.

On the bright side, some of these are steam tunnels, which means they'll be extra-cozy in winter. On the not so bright side, they have operating hours, unlike the buildings themselves, so any late-night cramming session during finals time will necessarily involve walking through the snow.

I am not sure if our school has drains, which I have heard is also a good place to explore in the winter, but those are definitely not sanctioned and will require a lot of time and effort and luck to discover.

Roofs, however, are open (free?) to people who find the doors open at the right time. It is apparently not a rare occurrence. I have yet to be on a roof but that should be fun too.

. . .

Boys are weird creatures. I am sure this has been stated before (I vaguely remember this particular statement or a variation of it on my blog, and possibly on Kathrya's blog too although I can't remember if either is true), and I am aware it is a gross generalization, so I will restate this. Some of the boys I have encountered lately are weird.

The other day I went to the basement of the math and science building, and these two guys were selling white coffee to fundraise for some student group (I think it was Malaysian or some other Southeast Asian group, the guys told me but I don't quite remember). I asked them what white coffee was, and one of the guys explained (different coffee brewing process + condensed milk), and then took off the "$1" sign and said that they were running low anyway, so he gave me a free sample. Then they packed up so quickly and left the table before I even left.

Today, as I was walking down the escalator, one of the guys in my class walked past me, obviously in a hurry. He then held the door open for me, even though I was not even close to the door, so I half-ran to get the door so he wouldn't wait too long.

Maybe the midterms are addling with their brains.

I would love to extend this to girls too so this doesn't resemble a gender stereotype, but unfortunately I am not meeting enough previously-not-well-known-and-probably-will-never-know-well girls to have any concrete examples.

. . .

Thanksgiving weekend was good. It involved lots of fish (alive, raw, microwaved, hot-potted, stuffed-toy-ified), a trip to the depths of Chinatown, friend-visiting, mall-bridge-hopping, movies (some good, some dreadfully slow), and a variety of other things that may or may not be appropriate to put on here. A blackboard was acquired, kitties were petted, and a bunch of pretty much useless RAMs and hard drives were lugged back up the hill.

I might write about it, but definitely not from my perspective and not with any clear-defined names.

And we can also definitely glaze over the late-night drunk on deliriousness hours of insanity.

It was apparently also Denise's birthday on Thanksgiving weekend. It was a rather sad event for her, at least on the day of her birthday, because none of us were there (Sam went to her cottage, other people were otherwise occupied with their families) and she was sick. To make matters worse she spent the weekend at the studio working on one of her many, many projects.

Sam organized a belated celebration for her by taking her to a dumpling place (and inviting all of us). They were really good dumplings (I haven't really had a vegetarian dumpling in a long while, and the ones there were delicious), and Denise and Sam ate two platefuls. I would have ordered a plate myself, but earlier that day I had gone to the-dorm-with-a-good-caf and had gotten myself onion rings and cheesecake and chicken and noodles and broccoli and iced tea, and normally I could have dealt with the main meal but the combo of onion rings and cheesecake was rather filling already, so I was stuffed by the end of the meal.

So not many dumplings for me. So sad.

. . .

I am really tired now. I slept at 4 in the morning, because I wanted Yuma to read me a chapter from a story and he didn't want to, so I stayed up doing silly things. This is probably directly related to my inability to attend my java class this morning, which apparently was pretty silly too, so it all balances out.

I bought four books from the book fair yesterday, all on math and science, and I can't wait to read them. I also signed up for about a million email lists from various clubs around my school, and plotted them all on my calendar in hopes that by virtue of them being there, I will do them.

So far I have not gone to the computer-recycling club, nor the outdoors excursions club, but I have asked Jessica about the two competitions I was interested in (both require teams).

Maybe if I sleep more...

Weekends

Last weekend (it seems so far away even though it's only Tuesday), I went on a camping trip with a group of fellow engineers (and other people, who were mainly engineers' girlfriends/boyfriends). We left on what must be one of the most awful days to leave for a camping trip: it was rainy and cold. But luckily, we had plenty of firewood (and people bought even more after they got drunk), lots of food, and enough alcohol to put a liquor store to shame (we had plenty of cases of all sorts of beer, and other things people brought like rum and gin and vodka, and our coordinator brought boxes of wine).

I was probably one of the few (if not only) people who did not drink, but the food was really good. Our coordinator made chili, and we roasted spider weenies over the fire (and accidentally dropped what was probably an entire pack of hot dogs into the fire) and made s'mores until we ran out of chocolate and biscuits. Someone even roasted a pepper (and said, "It smells really good!" so everyone took turns smelling it).

I had way too much food for the night (I think maybe 4 or 5 hot dogs plus a ton of marshmallows and a tub of chili), but it was so good I couldn't stop eating. I probably burned all of the excess calories off during the night though, when I was freezing so badly I had a blanket wrapped around me, a down jacket on, and was still shivering through much of the night.

We talked about a bunch of silly things, like previous trips the other people had gone on, air force experience (a lot of people in our group had been in the army in some way), and generally Islandtown and other places. Then people started making up really dirty limericks and singing lewd songs, and cigars got passed around. I didn't like the smoke, plus I had drank too much lemonade, so I joined the bathroom excursion.

We hiked down the road, through many, many puddles (my boots are all disgusting now), and arrived at the bathrooms. When we got out, we saw that there was a playground nearby, so our temporarily appointed VP Acquisitions (we had VPs for almost everything, from VP Fire to VP Innuendo) decided it was a great idea to steal two of the kiddie cars in the playground (apparently the goal of VP Acquisitions was to get a golf cart, but that was too difficult), so two of the girls hauled the cars to our campfire.

I spent the rest of the night warming myself by the fire and stopping myself from eating more food. So obviously when I got up in the morning I went right back to the fire and, as the bacon was the only thing ready, I ate bacon. We had all forgotten to turn off the propane stove the night before, so we only had a little bit of propane left. Someone suggested we cook bacon over the fire, so we did that (in a pan and not on a stick, sadly). There was also instant oatmeal made in such huge batches that it looked almost homemade.

I must have ate 8 strips of bacon. So. Much. Food.

Then the group of girls I shared a tent with (and one of their friends and her boyfriend) decided to take a walk to the lake, and when we got there we wanted to walk around the lake. So we hiked through mountains of trash and sand and long reeds, and got to see the lake from all angles. When we got back, there was spaghetti cooking on the fire (food was definitely one of our themes), and it was delicious too. Too bad we had to leave soon after, but not before we finished the rest of the marshmallows, all of the beer, and someone roasted a banana.

On our way back, we talked about more trips (including a skiing trip that I'd love to go on), deteriorating bridges ("please don't stop under the bridge!"), and people who drank too much beer and needed to go to the bathroom (one guy was almost desperate enough to emulate Mario). If it were any warmer and drier I would have wished it lasted longer. As it were though, I was plenty glad to return to my warm, cozy room and actually sleep on a proper bed.

. . .

Next weekend I am going on another trip, except this time I am going to Beavertown (I had bought the tickets last weekend, and I am so excited). I already have my outfits planned out, because, obviously, this is the most important part. Well, also because Yuma said he would be in charge of planning the events, so that does not leave me with much left to plan for.

I told this to a guy I had met online a couple weeks ago (who knew about my situation with Yuma), and he said, "Bring pepper spray."

I hope I won't ever have to use that.

That aside, I am really, really excited. I'm hoping I will finish all of my homework before Friday, and then maybe skip out of my last class on Friday so I don't need to be at the bus station at 12 in the morning (although that is also a feasible option, if I had to), and then I'll skip my Tuesday tutorial so I can have three and a half days (and four nights!) in Beavertown.

But that means I have to work now, so off I'll be.