Wednesday, April 13, 2005
well. i think i cleared my first hurdle by the skin of my teeth. hopefully still in contension for A- (and of the uninitiated, our math dept is really very stingy about giving anyone higher than a B+ for their honours thesis). well i personally thought the talk went quite well and some friends told me it was great but of course, due to the nature of the subject material, those highly brilliant ones like hanmao felt it was too BORING. =) well to each his own right?then following the talk, i was given a 10 minute break before my interview, which thankfully was held in tkm's office. a place i've already grown accustomed to. lst started the interview asking me to show him the matrix associated with type A_4 graph which i did pretty easily and then he asked me to explain how the finite reflection groups must necessarily have positive definite graphs which i think i did with ease as well. i think that was all he asked. then tkm started to ask. he asked me about how the orthogonal transformation must have with it an associated matrix that is orthogonal. fumbled a bit before i managed to get teh answer. then on a related note he asked me for the converse to some statement i wrote. luckily i preempted that question so i answered it without thought. then came the difficult part. he asked me if every reflection was diagonalizable. horro of all horrors. linear algebra!!! something with i took years ago. sweat started to trickle down my forehead. literally. i was so completely stumped. anyway after bluffing my way through by saying that all reflections must have symmetric matrices and therefore definately diagonalisable, tkm asked me to consider a basis and to tell him what basis i would consider. thankfully i caught the hint then and managed to give a rather shaky but correct answer.
then for the second last question, tkm asked me if any other element in a FRG would also hence be diagonalisable. after going through the education system, it is perhaps instinctive that the answer is no. but i just could not justify why. so lst hinted that i should consider eigenvectors and eigenvalues. again!! linear algebra!! i must have completely forgotten about linear algebra even though we studied eigenvectors and eigenvalues in jc!! but thankfully i remembered some of the properties and eventually gave another correct by unconfident answer. then the killer question came. tkm sed "so now we know non-reflection elements cannot be diagonalisable over R so are they diagonalisable over C?" that one i was completely stumped. then tkm turned to lst and they both laughed and tkm said to lst "actually i don't think he would know that property." so they decided to just explain the answer to me. and that was the end.
ahhhh. so refreshing now after the interview. supposed to see tkm today to get back my paper so that i can make changes for the final submission. going to give myself a break today and relax a bit before starting to up the pace towards the exams. everytime i walk into my room i see this poster on my wall.
inspiration. i will perform a terence-logic triple this semester. ok i won't be able to do it if i continue typing this entry so that's all folks. ciao!
{10:17 AM}
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