Tori's Transition Matrices
Transition Matrices
The idea of transition matrices is to use the matrices to accurately predict the "future" distribution of quantities. After some predetermined “switching” or “transitional” behavior is applied to some number of the things over a series of generations of “switching.”
In a transition situation it is imperative to create you “initial condition” matrix as a row matrix, with heading for columns matching the transition matrix.
The example Mr.M gave us had to deal with Vehicle Purchase Patterns. He made us draw out a “transitional diagram” that looks like Figure 1. Remember the “Loopie” always goes back to itself!
A. C T V
C 0.89 0.04 0.07 =1.0
T 0.02 0.95 0.03 =1.0
V 0.05 0.08 0.87 =1.0
Consider at the beginning of this situation, the known distribution of vehicle buyers, is as such:
Cars- 60000
Trucks- 80000
Vans- 75000
*The number total in this example is STATIC value!
B. Now… C T V
60000 80000 75000
So, Now we actually have to do the math:
1 x 3 3x3
B A
Row Matrix’s = 1 x N
X
Transition Matrix’s = N x N
So in the future, the values in the “answer” Matrices will ALL stabilize to some value…
In this Case B x A ^100 , and then compare to B x A ^101, we can see that the values come together and equal
C T V
44975 118469 51556
Enjoy reading this blog it took forever, and always remember Matrix Multiplication is NOT Commutative!
Figure 1 below:
The idea of transition matrices is to use the matrices to accurately predict the "future" distribution of quantities. After some predetermined “switching” or “transitional” behavior is applied to some number of the things over a series of generations of “switching.”
In a transition situation it is imperative to create you “initial condition” matrix as a row matrix, with heading for columns matching the transition matrix.
The example Mr.M gave us had to deal with Vehicle Purchase Patterns. He made us draw out a “transitional diagram” that looks like Figure 1. Remember the “Loopie” always goes back to itself!
A. C T V
C 0.89 0.04 0.07 =1.0
T 0.02 0.95 0.03 =1.0
V 0.05 0.08 0.87 =1.0
Consider at the beginning of this situation, the known distribution of vehicle buyers, is as such:
Cars- 60000
Trucks- 80000
Vans- 75000
*The number total in this example is STATIC value!
B. Now… C T V
60000 80000 75000
So, Now we actually have to do the math:
1 x 3 3x3
B A
Row Matrix’s = 1 x N
X
Transition Matrix’s = N x N
So in the future, the values in the “answer” Matrices will ALL stabilize to some value…
In this Case B x A ^100 , and then compare to B x A ^101, we can see that the values come together and equal
C T V
44975 118469 51556
Enjoy reading this blog it took forever, and always remember Matrix Multiplication is NOT Commutative!
Figure 1 below:
posted by Ryan Maksymchuk at
10:05 AM
1 Comments:
Tori,
I know I've said it in class...but great post! I can see the effort you put in, especially with the great diagram. Sometimes when we're out of our 'comfort zone' with technology, it's easy to get lazy and do the minimum (me included). You definitely didn't do that here, and for the record, I'm really proud of what you created. Your classmates are lucky....
RM
By
Ryan Maksymchuk, at 7:46 PM
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