Called LA2 because I had an older version called LA1.5, now obselete.
Click here for the notes
Well I compiled this by picking different bits from my revision notes then some careful fixes and some effort to make it smooth. The beginning two-third is a basic linear algebra course, and the last one-third is an advanced but interesting topic to cover: linear programming.
My general principle to arrange the contents is to solve three main problems: to compute the inverse of a matrix, the geometric implication of linear transformations, and the duality principle in linear programming. Some external guidance are also taken, like the classic Linear Algebra from S. Lang.
Multiple references are taken, see p.3 of the text. I've taken [copied] some exercises from those references as well.
Ch.1 Basics: vector and matrix arithmetic
Ch,2 Linear system: reduction, independence, dimension
Ch.3 Geometry I: orthogonality, projection
Ch.4 Determinants: implication in lower dimensions, elementary matrices, matrix inverse, Cramer's rule
---
Ch.5 Abstract vector space: axioms, function space, inner product space
Ch.6 Linear Transformation: coordinate mapping, change of basis
Ch.7 Eigenvectors: diagonalization, applications
Ch.8 Special operators: Hermitian, unitary operators, orthogonal diagonalization, spectral decomposition
---
Ch.9 Geometry II: affine space, convex sets, cones
Ch.10 Polytopes and polyhedrons: V-H characterization, Fourier Motzkin elimination
Ch.11 Linear programming: Farkas Lemma, separation, simplex, duality
It was not the main motivation to get the old 1.5LA revamped, but actually I'm writing this for one of my dear friend who is studying computer science who is getting stuck with them, and I hope that there will be more readers other than him :)
Monday, 21 December 2015
Wednesday, 4 November 2015
04-11-2015
Baseball oh baseball.
Another wonderful season has just ended. A late congratulation to Lamigo monkeys who gave a blessed display in G5-G7, the no hitter has been stunning and it was unimaginable that he had just played as a relief pitcher in the last game. Whilst on the opposite side of the globe, Cubs fans may have to wait another hundred years...
Baseball is the last sport that I've been paying attention to its professional leagues, other than football. That's a nice complement out of the football season after all, but that isn't the end of the story. They are completely different in nature.
Football, I am not sure if all of you would agree, is a chaotic process in nature. From the extremely wide varieties of tactics that leads to rigidity in substituting players, to a full dynamic process during the game, has made the whole season full of dependence and has random events leading all the way through. That doesn't seem to be obvious because every particular professional games has their strategy cautiously set up and ruthlessly executed, and being a full dynamic game the advantage accumulates --- and become decisive in the game. However looking the game in a more macroscopic way tells a different story. I learned that after following football for 10 years, and I bet it also took Abramovich also 8 years to realize that --- in 2012 --- the best team is not always going to win the champions league --- the phantom goal in 2005, the penalty showdown in 2006 and 2008, the Stamford Bridge massacre in 2009...and the against-all-the-odds display in 2012. It's the accumulation from the whole season that makes the slightest edge in the later stages of the Champions League. [Just a famous quote from zonal marking that I do agree quite a lot: semi-final of the champions League is always the most exciting, unpredictable, technically rich game in the whole tournament. And for me, being the semi-finalist is all about team strength and going any further requires a steel of mind with brilliantly delivered tactics, and loads of luck.]
Baseball however, has it quantity overwhelmed so that the game boils down onto data that really matters. Batter faces all sorts of pitchers and pitcher faces all kinds of batters, on a daily basis so the data representing their efficiency shows high correlation with their real performance. AVG [well some may think that being not very useful, especially for Moneyball fans], OBP, OPS --- accurately measures how efficient they score; ERA, H/9, WHIP --- predicts how likely pitches are going to allow runs. Whether it is a 100 mph 4-seam blitz, or a nasty curveball --- it does not matter --- in long run. Teams with proper farms may substitute a player by another without much difficulty, perhaps a drop of .05 in OBP, no one is really untouchable statistically. Drafting and exchange market, FA system, money and players lurking around --- definitely not the so called 'traditional' way in sports industry huh? But that's not the reason I love baseball. Taking a closer look into the game every single duel between the batter and the pitcher must be the star of the game. Look at the mind battle between them, their logical reasoning and physical reaction [baseball is 90% physical, and the other half is mental.], how can't you love that?
Two sports from two different culture, starring two different aspects in nature. I don't expect many to follow both as I do, but that will be on my recommended list seriously.
Oh, of course professional leagues aren't all of the sports available. We always have something called a union --- once again big, big congrats to the All Blacks, who again gave an astonishing display throughout. Hopefully I will have the honor to watch it live in Japan, 2019.
Hopefully.
Another wonderful season has just ended. A late congratulation to Lamigo monkeys who gave a blessed display in G5-G7, the no hitter has been stunning and it was unimaginable that he had just played as a relief pitcher in the last game. Whilst on the opposite side of the globe, Cubs fans may have to wait another hundred years...
Baseball is the last sport that I've been paying attention to its professional leagues, other than football. That's a nice complement out of the football season after all, but that isn't the end of the story. They are completely different in nature.
Football, I am not sure if all of you would agree, is a chaotic process in nature. From the extremely wide varieties of tactics that leads to rigidity in substituting players, to a full dynamic process during the game, has made the whole season full of dependence and has random events leading all the way through. That doesn't seem to be obvious because every particular professional games has their strategy cautiously set up and ruthlessly executed, and being a full dynamic game the advantage accumulates --- and become decisive in the game. However looking the game in a more macroscopic way tells a different story. I learned that after following football for 10 years, and I bet it also took Abramovich also 8 years to realize that --- in 2012 --- the best team is not always going to win the champions league --- the phantom goal in 2005, the penalty showdown in 2006 and 2008, the Stamford Bridge massacre in 2009...and the against-all-the-odds display in 2012. It's the accumulation from the whole season that makes the slightest edge in the later stages of the Champions League. [Just a famous quote from zonal marking that I do agree quite a lot: semi-final of the champions League is always the most exciting, unpredictable, technically rich game in the whole tournament. And for me, being the semi-finalist is all about team strength and going any further requires a steel of mind with brilliantly delivered tactics, and loads of luck.]
Baseball however, has it quantity overwhelmed so that the game boils down onto data that really matters. Batter faces all sorts of pitchers and pitcher faces all kinds of batters, on a daily basis so the data representing their efficiency shows high correlation with their real performance. AVG [well some may think that being not very useful, especially for Moneyball fans], OBP, OPS --- accurately measures how efficient they score; ERA, H/9, WHIP --- predicts how likely pitches are going to allow runs. Whether it is a 100 mph 4-seam blitz, or a nasty curveball --- it does not matter --- in long run. Teams with proper farms may substitute a player by another without much difficulty, perhaps a drop of .05 in OBP, no one is really untouchable statistically. Drafting and exchange market, FA system, money and players lurking around --- definitely not the so called 'traditional' way in sports industry huh? But that's not the reason I love baseball. Taking a closer look into the game every single duel between the batter and the pitcher must be the star of the game. Look at the mind battle between them, their logical reasoning and physical reaction [baseball is 90% physical, and the other half is mental.], how can't you love that?
Two sports from two different culture, starring two different aspects in nature. I don't expect many to follow both as I do, but that will be on my recommended list seriously.
Oh, of course professional leagues aren't all of the sports available. We always have something called a union --- once again big, big congrats to the All Blacks, who again gave an astonishing display throughout. Hopefully I will have the honor to watch it live in Japan, 2019.
Hopefully.
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