TA Bong_Lee>>so can u catch up now?
Ka Wai--Chan>>hello
Shuk Fan--Chau>>good evening everybody
Hiu Nga--Cheung>>i have many????
TA Bong_Lee>>than ask please!
Hiu Nga--Cheung>>why can't i copy and paste in the chatting row
Hiu Nga--Cheung>>i mean the white row below
TA Bong_Lee>>i can
Hiu Nga--Cheung>>how come
TA Bong_Lee>>do u have any mathematics problem?
Hiu Nga--Cheung>>yes
Hiu Nga--Cheung>>last section in chap.2
TA Bong_Lee>>which part?
Chun Pong--Derek--Chow>>use ctrl+c to copy it
Hiu Nga--Cheung>>what is ctrl+c
Hiu Nga--Cheung>>what is c
Chun Pong--Derek--Chow>>the keyboard
Hiu Nga--Cheung>>then how to paste
Prof Yan--Min-->>Hello! Again I see only students from Holap.
Prof Yan--Min-->>Have you read throught onto and one-to-one?
TA Bong_Lee>>ctrl+v
Chun Pong--Derek--Chow>>x-cut, c-copy, v-cut
TA Bong_Lee>>in http://algebra.math.ust.hk/matrix_linear_trans/05_composition/lecture2.shtml
TA Bong_Lee>>there is a typing error
Hiu Nga--Cheung>>my? is
Hiu Nga--Cheung>>T: Rm Õ Rn and S: Rk Õ Rn
Hiu Nga--Cheung>>TS: Rk Õ Rn
TA Bong_Lee>>the i-j entry =ith row * jth col
Prof Yan--Min-->>Do you mean the dim of R* is wrong?
Hiu Nga--Cheung>>may you see the note instead of what i type
Hiu Nga--Cheung>>composition and matric multiplication
Prof Yan--Min-->>Yeah, I got it. T is from R^n to R^m. TS is from R^k to R^m. Thank you
Hiu Nga--Cheung>>part 3
Hiu Nga--Cheung>>do u type the wrong thing Prof
Hiu Nga--Cheung>>in the note
Prof Yan--Min-->>Where in part 3?
Prof Yan--Min-->>I just saw the same error in the proof in part 3
Prof Yan--Min-->>Thank you
Hiu Nga--Cheung>>there are many TS: Rk Õ Rn
Prof Yan--Min-->>When did you find the error?
Hiu Nga--Cheung>>two days ago
Hiu Nga--Cheung>>that's why i have so many????
Prof Yan--Min-->>It would be better if you can e-mail me or post on the BBS as soon as you find the error.
Prof Yan--Min-->>The sooner the error is corrected, the less confused for the other students.
Prof Yan--Min-->>I will make correciton tomorrow
Hiu Nga--Cheung>>i haven't thought that same error occur in so many place
Hiu Nga--Cheung>>so i think it is correct one
Prof Yan--Min-->>Well. The problem of cut and paste :-)
Hiu Nga--Cheung>>ok
Hiu Nga--Cheung>>AB = [TS(e1) TS(e2) ... TS(ek)]
Hiu Nga--Cheung>>what is that mean
Prof Yan--Min-->>AB is defined as the matrix of TS. Right?
Prof Yan--Min-->>Please answer my Q first.
Hiu Nga--Cheung>>yes
Prof Yan--Min-->>Now apply the theorem in http://algebra.math.ust.hk/matrix_linear_trans/02_linear_transform/lecture5.shtml
Prof Yan--Min-->>Take A to be AB. T to be TS
Prof Yan--Min-->>Got it?
Hiu Nga--Cheung>>no
Prof Yan--Min-->>The theorem on part 5 of section 2.2 says
Hiu Nga--Cheung>>yes i got it
Prof Yan--Min-->>Good!
Prof Yan--Min-->>One key thing you need to keep in mind about chapter is the translation between matrices and linear transformaitons
Prof Yan--Min-->>Chapter 2. Sorry
Hiu Nga--Cheung>>but what is T(e1) T(e2) ... T(en) means
Prof Yan--Min-->>For R^3, e_1 = (1, 0, 0), e_2 = (0, 1, 0), e_3 = (0, 0, 1)
Prof Yan--Min-->>The e_i for other R^n is similar.
Prof Yan--Min-->>T(v) is the transformaiton T applied to v
Prof Yan--Min-->>T(e_1) is transformation T applied to e_1
Hiu Nga--Cheung>>why are they multiply together
Prof Yan--Min-->>They are not multiplied together[T(e_1) T(e_2) T(e_3)] is a matrix with T(e_1) as [col 1], T(e_2) as [col 2]
Prof Yan--Min-->>There is a space between them. It is similar to A = [a_1 a_2 ...] where a_1 is [col 1] of A etc
Hiu Nga--Cheung>>then what isB = [S(e1) S(e2) ... S(ek)].
Prof Yan--Min-->>Because B is the matrix of S
Hiu Nga--Cheung>>B is in AB
Prof Yan--Min-->>Do you understand my answer? B is the matrix of S
Hiu Nga--Cheung>>[T(b1) T(b2) ... T(bk)] = [Ab1 Ab2 ... Abk],
Hiu Nga--Cheung>>where do the A come from
Prof Yan--Min-->>Because A is assumed to be the matrix of T, so T(x) = Ax.
Prof Yan--Min-->>do you understand my answer?
Hiu Nga--Cheung>>yes
Prof Yan--Min-->>More Q?
Hiu Nga--Cheung>>Linear Transformation
Hiu Nga--Cheung>>part5
Hiu Nga--Cheung>>last example
Prof Yan--Min-->>What specific Q?
Hiu Nga--Cheung>>matrix for the rotation is cosü - sinü ]
Hiu Nga--Cheung>>sinü cosü
Prof Yan--Min-->>When vectors are used in matrix, they are supposed to be vertical
Hiu Nga--Cheung>>oh
Prof Yan--Min-->>I think I have mentioned that when vectors and matrices are mixed (like here, vectors as columns of matrix), you better write vectors vertically
Prof Yan--Min-->>See the very first page of chapter 2. http://algebra.math.ust.hk/matrix_linear_trans/01_vector_matrix/lecture1.shtml
Prof Yan--Min-->>Any Q from other students?
Prof Yan--Min-->>Don't be shy
Prof Yan--Min-->>Are all of you from Holap?
Hiu Nga--Cheung>>what is Holap
Chun Pong--Derek--Chow>>my school~
Siu Him--Lau>>I see nth in "Current Users". Is that my problem only?
Prof Yan--Min-->>Where are you from? Hiu Nga?
Hiu Nga--Cheung>>a school in shatin
Chun Pong--Derek--Chow>>i don't have your problem, but i see 2 of you
Prof Yan--Min-->>Anybody else in your school are in my class?
Hiu Nga--Cheung>>Baptist Lui Ming Choi
Hiu Nga--Cheung>>no
Hiu Nga--Cheung>>they are in physics class
Prof Yan--Min-->>It appears that only Holap and BLM are avtive in my class
Chun Pong--Derek--Chow>><===not so active
Prof Yan--Min-->>I do not recall that Hiu Nga was in last chatting session
Hiu Nga--Cheung>>i have test that time
Hiu Nga--Cheung>>revision
Prof Yan--Min-->>I see.
Prof Yan--Min-->>Have the students from Holap read through the material?
Chun Pong--Derek--Chow>>i know what the last chapter is saying, but still not so familiar in linear transformation
Prof Yan--Min-->>What is your specific problem with linear transformation
Prof Yan--Min-->>Which part of section 2.2, say.
Prof Yan--Min-->>Do you have difficulty with part 1?
Chun Pong--Derek--Chow>>no now, after i read the notes carefully
Chun Pong--Derek--Chow>>because i have done my test so badly
Chun Pong--Derek--Chow>>and the transformation.......i need more time
Prof Yan--Min-->>Please spend more time. You are falling behind the schedule
Chun Pong--Derek--Chow>>i will......SOR
Prof Yan--Min-->>Is my course more time consuming or more difficult than physics?
Prof Yan--Min-->>I am wondering whether web based linear algebra is suitable for busy form 6 students.
Chun Pong--Derek--Chow>>for me, it's just because i am not used to reading the notes on the computer
Chun Pong--Derek--Chow>>and the topics are in our pure maths syllabus
Prof Yan--Min-->>You think both the depth and the breadth of my course is suitable, at least so far\?
Chun Pong--Derek--Chow>>yes at least we can learn earlier than our classmates, and there's nothingbad
Prof Yan--Min-->>Do you feel time pressure? Hiu Nga?
Prof Yan--Min-->>How do you manage to read through the material? Maybe you have some tips for Holap students
Hiu Nga--Cheung>>tips
Hiu Nga--Cheung>>read one section each time
Hiu Nga--Cheung>>watching monitor hurts eyes
Hiu Nga--Cheung>>if i can choose, iwould like printed material
Chun Pong--Derek--Chow>> <====me too
Prof Yan--Min-->>But you lose the linking function
Hiu Nga--Cheung>>of course it is not so convinient, but easy to read
Hiu Nga--Cheung>>not so tired
Hiu Nga--Cheung>>and i don't like typing in chat room
Hiu Nga--Cheung>>my hands are out of control
Prof Yan--Min-->>Yeah. Before this course, I never did chatting. I thought it really stupid to talk by hand
Chun Pong--Derek--Chow>>and for maths, it's so troublesome to type the symbols, although i get used to it
Hiu Nga--Cheung>>i am not
Prof Yan--Min-->>Maybe we should install camera on our conputers and really talk to each other
Hiu Nga--Cheung>>then ust should sponsor me
Chun Pong--Derek--Chow>>yes!
Hiu Nga--Cheung>>i don't have camera
Prof Yan--Min-->>Although the technology is there, the timing is not ready.
Hiu Nga--Cheung>>the chatting room is so quite
Prof Yan--Min-->>Perhaps it is still to early for web based courses. At least some courses.
Hiu Nga--Cheung>>only 2 students talk??
Prof Yan--Min-->>Maybe the other students hate typing even more.
Chun Pong--Derek--Chow>>.......we are busy ma............i chat with you, at the same time, i am having dinner
Hiu Nga--Cheung>>really?\
Chun Pong--Derek--Chow>>just my guess
Hiu Nga--Cheung>>how many girls in this course?
Prof Yan--Min-->>Any girls from Holap?
Chun Pong--Derek--Chow>>fan
Chun Pong--Derek--Chow>>the pre-house captain
Prof Yan--Min-->>I do not get it. Please explain
Chun Pong--Derek--Chow>>she is Shuk Fan
Prof Yan--Min-->>what bout "pre-house captain"
Hiu Nga--Cheung>>did she chat
Shuk Fan--Chau>>don't say that, iam very nervous now!!!!!!!!!
Chun Pong--Derek--Chow>>have you prepared your speech, fan?
Shuk Fan--Chau>>i am preparing it now
Shuk Fan--Chau>>what should i say tomorrow?
Chun Pong--Derek--Chow>>for me in prefect, i talked about my past and my wish
Chun Pong--Derek--Chow>>you should emphyasis your contribution in green house in your speech
Shuk Fan--Chau>>but....
Shuk Fan--Chau>>is it strange for the house member?
Chun Pong--Derek--Chow>>you can say it indirectly. you can talk about your past in green house
Shuk Fan--Chau>>ok.......
Shuk Fan--Chau>>thanks
Chun Pong--Derek--Chow>>today is really quiet in the chatting room.........
Prof Yan--Min-->>Well. I need math questions.
Hiu Nga--Cheung>>yes i have ?
Hiu Nga--Cheung>>For each of the following matrix A, find all the matrices X satisfying AX = XA.
Hiu Nga--Cheung>> (1 2)
Siu Him--Lau>>which exercise?
Prof Yan--Min-->>Other students, please go to http://algebra.math.ust.hk/matrix_linear_trans/05_composition/exercise4_answer.shtml
Prof Yan--Min-->>If you want XA = AX, you must have A and X be square matrices ofthe same size.
Hiu Nga--Cheung>>have we prove this before
Prof Yan--Min-->>Let X be m by n. Let A be p by q.
Prof Yan--Min-->>AX makes sense only when q = m.
Prof Yan--Min-->>XA makes sense only when p = n.
Prof Yan--Min-->>So A is n by m
Prof Yan--Min-->>Then AX is n by n
Prof Yan--Min-->>And XA is m by m
Prof Yan--Min-->>For AX = XA, we must have m = n.
Prof Yan--Min-->>Conclusion: m = n = p = q
Prof Yan--Min-->>No Q from Holap?
TA Bong_Lee>>i want to ask
TA Bong_Lee>>is that AX=XA iff both A and X are linear transformation?/
Prof Yan--Min-->>Not necessarily. Try X is taking square and A is taking cube.
Prof Yan--Min-->>X and A are transformations from R to R
Prof Yan--Min-->>More Q? I do not mean Hiu Nga cannot ask Qs.
TA Bong_Lee>>then AX(x)=XA(x)=x^6??
Prof Yan--Min-->>Yes
TA Bong_Lee>>oh nothing!
Prof Yan--Min-->>More Q please.
Hiu Nga--Cheung>>what are you talking about ?
Hiu Nga--Cheung>>a take square?
Hiu Nga--Cheung>>x take cube
Prof Yan--Min-->>A(x) = x^2, X(y) = y^3
Prof Yan--Min-->>AX(t) = t^6, XA(t) = t^6
Hiu Nga--Cheung>>oh,
Prof Yan--Min-->>Everybody is waiting for the others to talk?
Hiu Nga--Cheung>>no
Prof Yan--Min-->>Then why so quiet?
Hiu Nga--Cheung>>i have'nt got any Q in my mind
Prof Yan--Min-->>Is my answer to your Q in the BBS OK?
Hiu Nga--Cheung>>what is BBS
Prof Yan--Min-->>Discussion board
Hiu Nga--Cheung>>ok
Hiu Nga--Cheung>>it seems only me posting something
Prof Yan--Min-->>You are correct, unfortunately
Hiu Nga--Cheung>>For linear transformations T, S: Rn Õ Rm, their addition T + S is defined by the formula (T + S)(x) = T(x) + S(x)
Hiu Nga--Cheung>>why
Prof Yan--Min-->>Yes
Prof Yan--Min-->>It is such a natural thing to do.
Prof Yan--Min-->>How do you add two functions together?
Prof Yan--Min-->>Say f(t) = 1 + t + t^2, g(t) = 2 - t + 3t^2
Prof Yan--Min-->>The formula is (f + g)(t) = f(t) + g(t) = (1 + t + t^2) + (2 - t + 3t^2) = 3 + 4t^2
Prof Yan--Min-->>We are doing the same thing in linear algebra
Hiu Nga--Cheung>>i haven't seen clearly the question
Hiu Nga--Cheung>>sorry
Prof Yan--Min-->>Is my answer satisfactory?
Hiu Nga--Cheung>>yes
Hiu Nga--Cheung>>how about our quiz last time
Prof Yan--Min-->>I have not looked at it yet. But I think you get a rough idea from my answers
Prof Yan--Min-->>I mean the answer sheet I distributed after the quiz
Hiu Nga--Cheung>>i have careless mistake in question 1
Hiu Nga--Cheung>>that make the whole question wrong
Prof Yan--Min-->>Then be more careful next time. Math is a good training on the patience and attention to details
Hiu Nga--Cheung>>i am leaving now ,bye
Prof Yan--Min-->>Only HJolap students are around. If you are still quiet, I will be leaving too.
Chun Pong--Derek--Chow>>ar yes
Chun Pong--Derek--Chow>>has the technical problem of wilde's web connection solved?
Prof Yan--Min-->>The technician is going to contact wilde directly.
Shuk Fan--Chau>>sorry, what problem?
Chun Pong--Derek--Chow>>thank you
Prof Yan--Min-->>Shuk Fan was not in Monday's chatting session?
Chun Pong--Derek--Chow>>she's there
Shuk Fan--Chau>>yes i'm there
Prof Yan--Min-->>Do you remember we talked about wilde could not participate in chatting?
Shuk Fan--Chau>>oh, i got that
Chun Pong--Derek--Chow>>i go now.......BYE everyone.....
Prof Yan--Min-->>No more Q. It is probably time to go. Bye
Shuk Fan--Chau>>bye
Shuk Fan--Chau>>have a nice dream!!!!!!!!!!!!!!!!!!