ec 402 (19/20) - lsepersonal.lse.ac.uk/sabharw5/lt04_helpwithcounting.pdf · lt wk4-help with fou...

EC 402 (19/20)

LT WK4 - HELP WITH fou NTNG

RAGVIR's SPEAKING NOTES

COUNTING is EASY But PEOPLE GET CONFUSED.

So HERE Is THE KEI INSIGHT :

- if someone says !LgI%Ei×8"

"

"

select a matrix P "

,etc

.

,

they are NOT asking for something trivial. Meaning

, say P is NXN, they are

actually asking youto specify N

'

separate equations - i. e. fill out every single element of P.

-

eg : say ⇐I:bf. imnh:1×Lf%,ILLweons

.a- - something

" £ ¥÷:Sounds obvious ? Well

, if so, great ! Because that's all there is to it

.

Let's see. . .

OUR SPECIFIC EXAMPLE

- Define E- 441 ⇒ is t -- 1%11%1 = 1¥!

2×2

Saywe set RP =3"

where I fqf.org;)- How

manyrestrictions does this embody?

filth = q , Equation I

abted = q ," 2

abt cd =

qz" 3

b 't d'

= q4" 4

but if q ,= qz lie IT is symmetric) ,

I restriction is redundant, right ?

[iii.%a9II.gg?e:r:h*af:#mmewns.f

GENERAL CASE

Due to the symmetry ,we will have as many restrictions as the

number Of terms excluding the lower triangular part of an NXN matrix.

X × X X. . -

O X XX . -

.

0 0 X X . - .

O O 0 X - . -

i i'

i :

rI r I

Terms : N;

N - I;

N -4N -3 - --It

Now,

remember how Gaussannoyed his math teacher in school ?

i. e. sum of integers from I to N ?

. . . Ike next slide )

① I + 2 + 3 +. . .

+ N

② N t N - I + N - Lt . . .

t I

① + ② ⇒ Htt Hi ) theft . -+ Inn )

: . I.IR = NII )2

SUMMAIY- number offor - redundant) qualities from a

" choose P sit. PikET "

style restriction.

! NINA)/2- Total number of qualities needed : Ni

- ADDITIONAL qualities needed :. : N7 NlN¥ = N(N

2