Squeaker (September 14)

Squeaker says:



Hello and how are you?
So I guess it’s my turn to be the scribe for today (September 14, 2006) so here it goes.

Transition Matrices

In this subsection of the unit on matrix modeling, we will predict the outcomes of ‘switching behavior’ examples using matrix multiplication techniques to track that behavior over time.

Applications: marketing
Air traffic control
Computer science (networking)
Etc.
Ex.
Students enrolled in mathematics (MB)

More useful format:
To
A C P
‾ ‾ *every row is a “1”
A .8 .14 .06 = 1.0 sum from C .02 .97 .01 = 1.0
P _ .11 .05 .84_ = 1.0


Yeah, so?
It would be worthwhile to know that at time (start) the distribution of students is:
A- 80 ‾
C- 30 - 180 PEOPLE
P- 70 _

Us a matrix [ ROW MATRIX!!]
A C P
B= [ 80 30 70]

Rules: (to find next cycle’s distribution)
Row Matrix- 1 X n Transition matrix- nXn
(“Initial condition”) (percentage breakdown by
( “market share” ) category w/”1” sums)
1X3 3X3

So, we get
[B] • [A] = [74 44 64]
1X3 3X3 1X3
* The total number of students is STATIC?

So, if need to see stability (and these problems ALWAYS stabilize), do this

* N.B.! [B] • [A] = Ans ( After 1st switch)
[B] • [A] ^ (large number n)
Compared to
[B] • [A]^ (n+1 one larger number)
We see stability in this example here: A C P
[24 139 17]




And for those of you that are still wondering what N.B. stands for it is an abbreviation for a Latin phrase nota nene. This means “note well” and is used to emphasize an important point. Also I hope this helps somebody, somewhere, somehow, sometime. Tomorrow it will be the turn of number 4 to scribe the notes for the day. My first blogging experience is now done and until next time see ya.
- Squeaker

Next scribe is Infedros