Matrix Theory, Representation and Computation for Programmers

First Technology Transfer Ltd

Course

Inhouse

Price on request

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Description

  • Type

    Course

  • Methodology

    Inhouse

  • Duration

    3 Days

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Course programme

Overview
The purpose of this course is to
  • refresh forgotten knowledge of those whose matrix theory is a "bit rusty"
  • describe and discuss various ways of representing matrices - both dense and sparse
  • describe various problems in computational geometry, numerical analysis, differential equation solving and signal processing which can be represented using matrix notation
  • describe algorithms and data structures for performing matrix operations efficiently
  • overview matrix computations using libraries such as scilab and matlab

Course Contents
overview of vectors
  • geometrical representation of vecors in 2D and 3D "
  • handedness
  • scalar and vector products
  • n-dimensional spaces
  • basis, orthonormal basis and orthogonalisation
matrices and determinants - the basics
  • basic concepts
  • identity and zero matrices
  • matrix sums and products
  • diagonal matrices
  • transpose of a matrix
  • symmetric and skew symmetric matrices
  • determinants and their evaluation
  • inverse of a matrix
  • orthogonal matrices
  • block matrices
  • triple product
  • matrix representation of a transformation
  • projection mapping
  • changing bases
  • isometries and orthogonal matrices
Review of Matrix Algebra
  • complex numbers
  • eigenvalues and eigenvectors
  • linear isometries in 3D space
  • rank and row operations
  • reducing a matrix to echelon form
  • inverting a matrix via row operations
  • diagonalisation
  • quadratic forms
  • Choleski decomposition
  • singular value decomposition (SVD)
C Data Structures and Algorithms for vector and matrix manipulation
  • Overview of C - arrays, pointers, and dynamic data structures
  • fixed point vs. floating point arithmetic
  • techniques for representing sparse matrices
  • srategies for code optimisation
  • strategies for taking advantage of parallelism on multi-processor architectures
  • overview of relevant code in "Numerical Recipes in C"
  • overview of Scilab's vector and matrix processing capabilities
  • overview of Matlab's vector and matrix processing capabilities
  • errors and error handling
C++ Data Structures and Algorithms for vector and matrix manipulation
  • advantages and disadvantages of C++ vs C
  • how efficient is C++ relative to C ?
  • devising C++ frameworks for performing vector and matrix operations and calculations at a higher level of abstraction
Some actual applications (can be tailored)
  • computer games
  • operations research
  • modeling and simulation

See related categories

Matrix Theory, Representation and Computation for Programmers

Price on request

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