Kardi Teknomo
Kardi Teknomo Kardi Teknomo Kardi Teknomo
   
 
  Research
  Publications
  Tutorials
  Resume
  Resources
  Contact

Visit Tutorials below:
Adaptive Learning from Histogram
Adjacency matrix
Analytic Hierarchy Process (AHP)
Analysis of Algorithm
ArcGIS tutorial
Arithmetic Mean
Aroon Oscillator
Bayes Theorem
Bootstrap Sampling
Bray Curtis Distance
Break Even Point
Chebyshev Distance
City Block Distance
Conditional Probability
Complex Number
Continued Fraction
CryptArithmetic
Data Analysis from Questionnaire
Data Revival from Statistics
Decimal to Rational
Decision tree
Difference equations
Digital Root
Discriminant analysis
Divisibility
Eigen Value using Excel
Euclidean Distance
Euler Integration
Euler Number
Excel Iteration
Excel Macro
Excel Tutorial
Expectation Maximization (EM) Algorithm
Factorial Function
Feasibility Study
Financial Analysis
Financial Education
Gaussian Mixture Model
Generalized Inverse
Generalized Mean
Geometric Mean
Ginger Bread Man and Chaos
Graph Theory
Growth Model
Hamming Distance
Harmonic Mean
Hierarchical Clustering
Independent Events
Incident matrix
Jaccard Coefficient
Kernel basis function
Kernel Regression
k-Means clustering
K Nearest Neighbor
LAN Connections Switch
Learning from data
Lehmer Mean
Linear Algebra
Logarithm Rules
Mahalanobis Distance
MapReduce
Market Basket Analysis
Mean Absolute Deviation
Mean and Average
Mean, median, mode
Minkowski Distance
Minkowski Mean
Monte Carlo Simulation
Multi Agent System
Maximum Likelihood
Multicriteria decision making
Mutivariate Distance
Neural Network
Newton Raphson
Non-Linear Transformation
Normalization Index
Normalized Rank
Ordinary Differential Equation
Page Rank
Palindrome
PI
Power rules
Prime Factor
Prime Number
Q Learning
Quadratic Function
Queueing Theory
Rank Reversal
Recursive Statistics
Regression Model
Reinforcement Learning
Root of Polynomial
Runge-Kutta
Scenario Analysis
Sierpinski gasket
Sieve of Erastosthenes
Similarity and Distance
Solving System Equation
Standard deviation
String Distance
Summation Tricks
Support Vector Machines
System dynamic
Time Average
Tower of Hanoi
Variance
Vedic Square
Visual Basic (VB) tutorial
What If Analysis

 

Matrix-Set

By Kardi Teknomo, PhD.

< Previous | Index | Next >

Matrix-Set

To derive the formulation in the paper, we use a combination of both matrix and set operations. In contrast to ordinary matrices in linear algebra whose elements are numbers or scalar values (which we call matrix-count), it is necessary to create our own mathematical concept of a matrix-set which is a matrix whose elements are sets. We use tilde on the top of a matrix to indicate matrix-set, such as Flow-set matrix and OD-set matrix. Operations on matrix-set are similar to both operations in matrix and set theory where the members in each matrix element must be unique and the order of the elements in a set is not important. We also extend the Hadamard multiplication to involve a matrix-set and a binary matrix. The Hadamard product between a matrix set and a binary matrix is computed by multiplication of corresponding elements, resulting either in the original element of the matrix set (if multiplied with 1) or an empty set (if multiplied by 0).  We have developed special numerical library of matrix-set to serve the purpose of this research.

 

< Previous | Index | Next >

 

Share and save this tutorial
Add to: Del.icio.us  Add to: Digg  Add to: StumbleUpon   Add to: Reddit   Add to: Slashdot   Add to: Technorati   Add to: Netscape   Add to: Newsvine   Add to: Mr. Wong Add to: Webnews Add to: Folkd Add to: Yigg Add to: Linkarena Add to: Simpy Add to: Furl Add to: Yahoo Add to: Google Add to: Blinklist Add to: Blogmarks Add to: Diigo Add to: Blinkbits Add to: Ma.Gnolia Information

 

These tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi. (2013) Relationship between Generalized Origin Destination and Flow Matrix – A Tutorial
http://people.revoledu.com/kardi/research/trajectory/od/

 

 
© 2007 Kardi Teknomo. All Rights Reserved.
Designed by CNV Media