MATH303-18S2 (C) Semester Two 2018

Applied Matrix Algebra

15 points

Details:
Start Date: Monday, 16 July 2018
End Date: Sunday, 18 November 2018
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 27 July 2018
  • Without academic penalty (including no fee refund): Friday, 12 October 2018

Description

A continuation of 200-level linear algebra with computational and theoretical aspects and applications.

This course looks at how matrix algebra can be applied to solve a variety of problems in commerce, data science, engineering, operations research, and elsewhere.  The course has three main sections: orthogonal decomposition, positive definiteness, and linear programming.  Applications are explored in some depth.

Learning Outcomes

  • Students who completely master the course material will:

    Be knowledgeable of
  • The Frobenius and other matrix norms.  Orthogonal (including Householder and Givens) and unitary matrices.  The QR factorization.  Projection and orthogonal projection matrices;
  • The singular value decomposition, low rank approximations, total least squares, and the Moore-Penrose pseudo-inverse;
  • Linear programming and applications, revised simplex, artificial variables, shadow prices, duality, degeneracy, Bland’s anti-cycling rules, the integer solution property of integer transportation problems, integer and logical variables;
  • Positive definiteness, congruence, the modified Cholesky factorization.  Quadratic forms, equality constrained quadratic programming.

    Be able to use techniques from the course (including MATLAB where appropriate) to
  • Calculate the QR factorization of a matrix via Givens and via Householder matrices;
  • Find least squares / shortest solutions via the QR factorization and the SVD;
  • Find orthogonal bases for the range and null spaces of a matrix;
  • Find the total least squares fit to a set of data points via the SVD;
  • Form linear programming models of data fitting (one and infinity norm), blending, transportation, rostering, resource allocation, stock cutting, and similar problems.
  • Put a linear program into standard form, obtain an initial basic feasible solution via artificial variables, and then solve the original linear program via revised simplex;
  • Solve an integer linear or mixed integer linear program via branch and bound;
  • Identify a positive definite matrix by calculating its’ modified Cholesky factorization;
  • Categorize stationary points of multivariable functions via the Hessian;
  • Find the minimizer of a real valued complex quadratic;
  • Solve equality constrained quadratic programs.
    • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Critically competent in a core academic discipline of their award

      Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

Prerequisites

Restrictions

MATH352, EMTH412

Course Coordinator / Lecturer

Christopher Price

Textbooks / Resources

Recommended Reading:
•Noble and Daniel, "Applied Linear Algebra". Third edition.
•Strang, "Linear Algebra and its Applications".
•Fletcher, "Practical Methods of Optimization".

Indicative Fees

Domestic fee $749.00

International fee $3,788.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH303 Occurrences

  • MATH303-18S2 (C) Semester Two 2018