Principles of Mathematics in Operations Research

66 4 Eigen Values and Vectors

coefficient of 0.04 Blue 2 targets/Red 1 firer per unit time and 0.01 Blue 2
targets/Red 2 firer per unit time. The first Red unit is under directed fire from
both Blue units, with an attrition rate coefficient of 0.05 Red 1 targets/Blue
1 firer per unit time and 0.02 Red 1 targets/Blue 2 firer per unit time. The
second Red unit is subjected to directed fire from only Blue 1, with an attri-
tion rate coefficient of 0.03 Red 2 targets/Blue 1 firer per unit time.
(a) Write down the differential equation system to represent the combat dy-
namics.
(b) Find the closed form values as a function of time t for X{, X\, Y±, Y$.
(c) Calculate X{, X\, Y{, Yj,t = 0,1,2,3,4,5.

Web material

http://149.170.199.144/multivar/eigen.htm

http://algebra.math.ust.hk/determinant/03_properties/lecturel.shtml

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http://cio.nist.gov/esd/emaildir/lists/opsftalk/msg00017.html

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http://college.hmco.com/mathematics/larson/elementary_linear/4e/

shared/downloads/c08s5.pdf

http://college.hmco.com/mathematics/larson/elementary_linear/5e/

students/ch08-10/chap_8_5.pdf

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http://en.wikipedia.org/wiki/Determinant

http://en.wikipedia.org/wiki/Eigenvalue

http://en.wikipedia.org/wiki/Hermitian_matrix

http: //en. wikipedia. org/wiki/Jordan_normal_f orm

http://en.wikipedia.org/wiki/Skew-Hermitian_matrix

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Methodes-Maths/white/math/s3/s3spm/s3spm.html

http://home.iitk.ac.in/~arlal/book/nptel/mthl02/node57.html

http://homepage.univie.ac.at/Franz.Vesely/cp0102/dx/node28.html

http://hyperphysics.phy-astr.gsu.edu/hbase/deter.html