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For a collection of articles describing all aspects of semidefinite programming the following book is quite useful:

H. Wolkowicz, R.Saigal and L.Vandenberghe, "

*Handbook of Semidefeinite Programming*,*Theory, Algorithms and Applications"*, Kluwer, 2000 (A copy is left in Engineering library reserves section)

For general background on linear algebra, you can check any textbook on linear algebra. My favorite is the book by Horn and Johnson:

R.Horn and C.Johnson "

*Marix Analysis*", Cambridge University Press, 1985

In addition to basic linear algebra and matrix books you may wish to refer the following books for more specialized topics. The first one is for some topics which are important though not thoroughly treated in basic books (e.g. Kronocker products and sums, matrix polynomials, etc.)

R.Horn and C.Johnson "

*Topics in Marix Analysis*", Cambridge University Press, 1991.

For traetment of matrices from algorithmic and numerically stable point of view refer to

G.Golub and C.Van Loan "

*Matrix Computations*", Third Edition, Johns Hopkins University Press, 1996.

For applications of semidefinite programming refer to

L.Vandenberghe, And S.Boyd, "Semidefinite Programming",

*SIAM Review,*38(1):49-95, 1996.

For applications of SOCP in Engineering see

L.S.Lobo, L.Vandenberghe, S.Boyd and H.Lebert, "Second Order Cone Programming", '

*Linear Algebra and Its Applications*", 284:193-228, 1998

The following paper of Lovasz is a great survey of SDP for combinatorial optimization problems

L.Lovasz, "

*Semidefinite Programming*", Lecture Notes.

The following paper contains information on many aspects of SDP, in particular SDP formulation of various eigenvalue optimization problems, combinatorial optimization, duality and interior point methods

F.Alizadeh "

*Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization*", SIAM J. on Optimization, Vol. 5, no. 1, 1995

For an introduction to Jordan algebras look a the Chapter 8 of the
"*Handbook of Semidefinite Programming*" and the
following paper

S. Schmieta and F. Alizadeh, "Associative and Jordan Algebras, and Polynomial Time Interior Point Algorithms for Symmetric Cones,

*Mathematics of Operations Research,*Vol 26, no. 3.

For a general survey of second order cone programming look at

F. Alizadeh and D. Goldfarb, "Second-Order Cone Programming", RUTCOR RRR Report number 51-2001, Rutgers University.