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(*) Problem 1 due Monday; Problems 2-6 due
Please hand in 2-6 on Monday if possible.
Problems 2-6 due on Friday, September 20.
(*) September 16-22 is British Columbia
Reconciliation Week at the PNE; classes
suspended Wednesday, September 18.
"I encourage everyone to participate."
-- Professor Stephen Toope,
President and Vice-Chancellor, UBC.
(*) Continue to diagonalize [1/2,1/3;1/2,2/3]
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Today:
Diagonalize [1/2,1/3;1/2,2/3] (HW 1)
you should make sure that you can do
this with any reasonable 2 x 2 matrix.
For an algorithm, see 3,000 Solved ...,
Section 16.3.
Theorem: Markov matrix has 1 as eigenvalue.
see Subsections 4.6.1 and 4.6.2.
see Stochastic Matrix, wikipedia (note they
use row vectors, not column vectors)
Theorem: Sum of eigenvalues = Trace
see Trace (linear algebra), wikipedia
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"From the late 19th century, until the end of
the 20th century, the government of Canada, in
collaboration with church groups, ran a system
of Indian Residential Schools.
Aboriginal children were often forcibly removed
from their families at a very young age, and
many spent their entire childhood in these
schools, where they suffered emotional, physical,
and sexual abuse. Many died there."
-- Dr. Linc Kesler,
Director, UBC First Nations House of Learning,
Our Truth UBC - September 18,
http://www.youtube.com/watch?v=xjXM5SSzJ-s&feature=youtu.be
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On September 18, UBC will suspend classes in
Vancouver so we can all connect to the powerful
testimonies heard at the Truth and Reconciliation
Commision.
"I encourage everyone to participate."
-- Professor Stephen Toope,
President and Vice-Chancellor, UBC,
Our Truth UBC - September 18,
http://www.youtube.com/watch?v=xjXM5SSzJ-s&feature=youtu.be
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Consider going to the PNE on Wednesday, Sept 18,
to participate in the TRC.
Feast on salmon and bannock!
Free admission!
http://www.trc.ca
"If a man dwells on the past, then he robs the
present; but if a man ignores the past, he may
rob the future."
- Master Po [Keye Luke], "Kung Fu" [TV program]
http://www.youtube.com/watch?v=IKH4nY4WlFY
%%%
Back to our regular program...
[ 1/2 1/3 ]
[ ] eigenvalues lambda = 1, 1/6
[ 1/2 2/3 ]
lambda = 1
[ -1/2 1/3 ]
A - lambda I = [ ]
[ 1/2 -1/3 ]
[ -1/2 1/3 ] [ v_1 ] [ 0 ]
[ ] [ ] = [ ]
[ 1/2 -1/3 ] [ v_2 ] [ 0 ]
(1/2) v_1 = (1/3) v_2 ; [ v_1; v_2] = [ 3/2; 1 ]
or [ 30/2; 10 ] or [-3; -2 ]
or [ .6 ; .4 ] or ...
%%%
Back to our regular program...
[ 1/2 1/3 ]
[ ] eigenvalues lambda = 1, 1/6
[ 1/2 2/3 ]
lambda = 1/6
[ 1/3 1/3 ]
A - lambda I = [ ]
[ 1/2 1/2 ]
[ 1/3 1/3 ] [ v_1 ] [ 0 ]
[ ] [ ] = [ ]
[ 1/2 1/2 ] [ v_2 ] [ 0 ]
v_1 = - v_2 ; [ v_1; v_2] = [ -1 ; 1 ]
or [ 10 ; -10 ] or [-3; 3 ]
or [ -.7 ; .7 ] or ...