Optimization Models
Home
Software
Links
Index
Contact
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

Representing temperatures at different airports as a vector

We record the temperatures at three different airports, and obtain the following table.

airport temperature ({}^o F)
SFO 55
ORD 32
JFK 43
;
alt text 

We can represent the temperatures on a single temperature axis. This is known as the dot representation of a vector.

The dot representation could become very confusing if there were three temperatures to plot for each day in the year.

alt text 

Alternatively, we can view the triple of temperatures as a point in a three-dimensional space. Each axis corresponds to temperatures at a specific location. The vector representation is still legible if we have more than one triplet of temperatures to represent. The vector representation cannot be viewed in more than three dimensions, that is, if we have more than three cities involved. However, the data can still be represented as a collection of vectors.