Optimization Models
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1. Introduction
1.1. Overview
1.2. Optimization Models
2. Linear Algebra
2.1. Vectors
2.2. Matrices
2.3. Linear Equations
2.4.  Least-Squares
2.5. Eigenvalues
2.6  Singular Values
3. Convex Models
3.1. Convexity
3.2. LP and QP
3.3. SOCP
3.4. Robust LP
3.5. GP
3.6. SDP
3.7. Non-Convex Models
4. Duality
4.1. Weak Duality
4.2. Strong Duality
4.3.  Applications
5. Case Studies
5.1. Senate Voting
5.2. Antenna Arrays
5.3. Localization
5.4. Circuit Design

Two orthogonal vectors

The two vectors in mathbf{R}^3:

x = left(begin{array}{c} 1 1 3 end{array}right), ;; y = left(begin{array}{c} 4 -1 -1 end{array}right)

are orthogonal, since

x^Ty = underbrace{1 times 4}_{x_1 times y_1} + underbrace{1 times (-1)}_{x_2 times y_2} + underbrace{(-1) times 3}_{x_3 times y_3} = 0.