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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