Question

matlab - computing the eigenvalue, eigenvector, and the stability age structure.. Actually, I'm using matlab to compute the Leslie Matrices.

Answer 1

A=[0 1 5; .3 0 0 ; 0 .5 0] % Leslie matrix

A =

0 1.0000 5.0000
0.3000 0 0
0 0.5000 0



% Calculate the eigenvalues and eigenvectors of A:


[V,D]=eig(A)



V =

0.9501 + 0.0000i 0.9270 + 0.0000i 0.9270 + 0.0000i
0.2800 + 0.0000i -0.1922 - 0.2609i -0.1922 + 0.2609i
0.1375 + 0.0000i -0.0559 + 0.1803i -0.0559 - 0.1803i


D =

1.0182 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.5091 + 0.6910i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i -0.5091 - 0.6910i


StAgeStr = V(:,2)/(sum(V(:,2)))


StAgeStr =

1.3465 + 0.1598i
-0.2342 - 0.4121i
-0.1124 + 0.2522i

Answer 2

B=[0 1 1; 2/3 0 0; 0 1/3 0] % Leslie Matrix


B =

0 1.0000 1.0000
0.6667 0 0
0 0.3333 0



% Calculate the eigenvalues and eigenvectors of A:


[V,D]=eig(B)

V =

-0.8021 + 0.0000i 0.5032 - 0.1002i 0.5032 + 0.1002i
-0.5634 + 0.0000i -0.7069 + 0.0000i -0.7069 + 0.0000i
-0.1979 + 0.0000i 0.4776 + 0.0951i 0.4776 - 0.0951i


D =

0.9491 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.4746 + 0.0945i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i -0.4746 - 0.0945i



StAgeStr = V(:,2)/(sum(V(:,2)))


StAgeStr =

1.8435 - 0.3317i
-2.5802 - 0.0481i
1.7367 + 0.3797i

Answer 3

@dan815

Answer 4

StAgeStru is actually the Stable Age Structure..

Answer 5

what is a leslie matrix

Answer 6

I also saw in my example text file that I could use the following command:

Note, for a complex eigenvalue lambda the command abs(lambda) gives its size.

but I don't know how it works

Answer 7

In applied mathematics, the Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology.

Answer 8

it's like a 3 x 3 matrix but solving for eigenvalues and eigenvectors remains the same.

Answer 9

your eigen values and eigen vectors are probably right

Answer 10

the questions I had were:

% 3) For each of the following matrices, find the dominant eigenvalue
% and the corresponding eigenvector, and the stable age structure

% a) A=[0 1 5; .3 0 0 ; 0 .5 0]
% Note, for a complex eigenvalue lambda the command abs(lambda) gives its size.

% b) B=[0 1 1; 2/3 0 0; 0 1/3 0]


so that's basically just inputing the matrices 1 by 1
Starting with

% a) A=[0 1 5; .3 0 0 ; 0 .5 0]

% Calculate the eigenvalues and eigenvectors of A:

[V,D]=eig(A)

and stability age structure

StAgeStr = V(:,2)/(sum(V(:,2)))

Answer 11

and that's how I got all the stuff above *points up*

Answer 12

StAgeStr = V(:,2)/(sum(V(:,2)))
why does this tell you stable age structture

Answer 13

ummmmm ._______.

Answer 14

% The "stable age structure" is the longterm fraction of the total
% population represented by each stage: take the dominant eigenvector
% and divide it by the sum of the entries in it

Answer 15

oh ok

Answer 16

wanna check another code? this one is for phase planes and plotting Juvie and Adult Populations

Answer 17

how come u didnt take the first eigen vector to be dominant

Answer 18

errr what?

Answer 19

the first eigen vector is a result of the dominant eigen value

Answer 20

so what should the command be?

Answer 21

OH! if I do the same thing but with 1 instead x.x

Answer 22

no i am asking you, how do you know which vector is the dominant eigen vector

Answer 23

is it not based of the dominant eigen value?

Answer 24

hold on it's in the

Answer 25

% Note that the "dominant" eigenvalue is D(2,2) and the corresponding
% eigenvector is V(:,2)

Answer 26

?

Answer 27

is my code off or something? O_O

Answer 28

hmm the D one is the dominant eigenvalue and the V is the corresponding eigenvector?

Answer 29

the dominant eigen value is 1,1

Answer 30

how is it 1,1?

Answer 31

you mean this entry? 0.9491 + 0.0000i

Answer 32

yeah, isnt it the highest power

Answer 33

if u look at some stages for example
D^2= [0.9..^2 0 0
0 (-0.4...+...i)^2 0
0 0 (-0.4..+...i)^2]

Answer 34

which eigen value will be playing the biggest role as the powers increase?

Answer 35

whoever has the highest value... so would the code be

StAgeStr = V(:,2)/(sum(D(:,1))) ?

Answer 36

>> StAgeStr = V(:,2)/(sum(D(:,1)))

StAgeStr =

0.9105 + 0.0000i
-0.1888 - 0.2562i
-0.0549 + 0.1771i

hmm?

Answer 37

dont forget to make the 2, 1 in V too

Answer 38

and use V not D since u said u have to divide by eigen vector sum

Answer 39

okay listen, i think theres something wrong with ur eigen values actually

Answer 40

StAgeStr = V(:,2)/(sum(V(:,1))) gives me something like this

>> StAgeStr = V(:,2)/(sum(V(:,1)))

StAgeStr =

0.6779 + 0.0000i
-0.1405 - 0.1908i
-0.0409 + 0.1318i

Answer 41

ogm my bad!! i was looking at your 2nd matric not ur first

Answer 42

yeah I posted two remember. Matrix A was my first post and Matrix was my second post. I was wondering if I inputted them correctly because they seem so straight forward to tweak the code and apply what the example file gave

Answer 43

StAgeStr = V(:,1****)/(sum(V(:,1)))

Answer 44

>> StAgeStr = V(:,1****)/(sum(V(:,1)))
StAgeStr = V(:,1****)/(sum(V(:,1)))
|
Error: Unexpected MATLAB operator.