T Nation

Math Question


#1

Hey I have 3 little simple math question if anyone can help. It's just lines that I dont understand.

first

Y is a line in a complex plan that is determined by the origin and the complex number given by the scalar product of 2 vector x and y. It is denoted by (x,y)

Now sigma varies over the line Y' (Y' is symmetric to Y by the x-axis) so that sigma=tz (t is real)
z= complex conjugate of (x,y)(with the line over) / absolutevalue((x,y)). It is the unit vector

everything is good but now they say
sigma*(x,y)=t*abs(x,y). They say this is real. I dont understand

Second
E(j=0,p) = summation for index j from 0 to p
P^(j)(u) is a polynomial in u with power j

E(j=0,p)E(l=o,p) 1/(j!l!)P^(j)(u)Q^(l)(u)*(sigma-u)^(j+l) gives
E(k=0,2p) E(j=0,k (1/(j!(k-l)!)) P^(j)(u) Q(k-j)(u)^k

last

There exist an ''n'' so that (n-1)x is smaller or equal than.. y.. smaller than nx
for arbitrary x real positive and arbitrary y

now
h=b-a
n is greater than 1/h. 1/n is smaller than h
there exist an integer m such as
m/n smaller or equal to ..a.. smaller than (m+1)/n. (this is a modified version of the theorem above)

now ''clearly'' (well not for me)
(m+1)/n -a is smaller or equal to 1/n is smaller than b-a.

the right side of this is obvious (stated before) but I dont see why (m+1)/n -a is smaller or eq. than 1/n

sorry if this is not entertaining. I'll post it in a math forum also.


#2

scan question for better legibility. can't promise I can help tho, I'm on coop right now so my math is rusty


#3

I think what they are trying to get at here is |x+j*y| = (x+jy)(x-jy)

Therefore the magnitude of a complex number is equal to the product of it with its complex conjugate (x^2+j xy - j xy - j^2y^2) = (x^2+y^2) which is a real number.

Complex conjugates will be symmetric about the real axis (x). This is invariable to a scaling such that a*|x+j*y| = a*(x^2+y^2)


#4

Ermm...what he said. :stuck_out_tongue:


#5

Answer is `bout tree-fiddy.


#6

Where's Planet Fitness now?


#7

42


#8

I'll take this opportunity to ask, "WTF is a Jasmincar anyway?"


#9

The quadratic sum of the equals, minus the offset complex matrix^3, over the root of the moon.

Cubed.

I think


#10

I see what you did there.


#11

Glad you do, because to be honest I have NO idea what is going on in this thread :wink:

Much respek to the OP and the posters who are actually able to help him. Wow. I always thought I was smart, but I guess I will have to convince myself I am a different kind of smart and pretend it carries over.


#12

Err whats the meaning of life again?


#13

there is an error. When I wrote this in 2) I meant The length 1(x,y)1 instead of the absolute value of (x,y) which both have the two bars.

I'll be back later


#14

Oh shit, that completely changes everything!

Sorry, still got nothing for ya


#15

Yes. The product of a complex number with its conjugate is always real.

Good answer.


#16

Found an error in my answer:

|x+j*y| = sqrt(x^2+y^2)

||x+j*y|| often refered to as the norm (or L2 norm as we are in 2D cartesian space) is the x^2+y^2 and it can be interpreted as the power in a signal. It will pop up a lot when doing detection or estimation of a deterministic signal in noise, specifically in terms of describing performance for various SNRs, where SNR is power of signal/power of noise.

What are you studying Jasmincar?


#17

You know that m/n <= a < (m + 1)/n. If you just look at the left hand part, and add 1/n you get
m/n + 1/n <= a + 1/n. Subtracting a from both sides we have m/n + 1/n - a <= 1/n, or
(m + 1)/n - a <= 1/n as required. You can treat <, > etc like an = for adding and subtracting, you just need to be careful when multiplying...


#18

thanks.


#19

ok so

sigma=tz= t*(complexconjugate(x,y)/I(x,y)I)
sigma*(x,y)=t*I(x,y)I/I(x,y)I
sigma*(x,y)=t

but they write sigma*(x,y)=t*I(x,y)I

I still missing something


#20