Full Title  Applied Linear Algebra 

Short Title  Applied Linear Algebra 









Description 

The subject covers the linear algebra required for postgraduate engineering courses. The learner will gain the expertise to interpret the linear algebra models used in the engineering literature. It will also enable learners to model problems using linear algebra methods. 
Indicative Syllabus 

Review solutions of linear equations using Gauss Elimination / Backsubstitution / Elementary Row operations / pivots / REF / GaussJordan elimination / RREF  Consistency and systems with unique/multiple/zero solutions  (Geometry of Solutions) (solutions of equations as points, lines and planes)  Complete solution to AX = B (column space containing b, rank and nullspace of A and special solutions to AX = 0 from row reduced R)
Matrix Algebra Review addition and multiplication of matrices and vectors and their transposes.  Inverse matrices. Calculation via Gauss Elimination. Invertibility.  Block multiplication
3D Vectors/Rotation  Inner product, length, orthogonality cosine rule/angles, cross product  Rotation matrices, Euler angles and noncommutativity  Projection, reflection, scaling  Lines / planes in 3 dimensions  Linear transformations and change of basis (dual basis)
Vector spaces and subspaces  Basis and dimension / linear independence and span  Four fundamental subspaces ( row, column, rightleft nullspaces, and their bases)
Least squares solutions, overdetermined systems (closest line by understanding projections)
Orthogonalization by GramSchmidt (factorization into A = QR) Orthonormal matrices (rotation matrices as)
Determinants / as volume / cofactor formula / applications to inverses / calculation via Gauss elimination
Eigenvalues / SVD  Eigenvalues and eigenvectors (diagonalizing and computing powers of matrices)  Matrix exponentials. Solving difference and differential equations  Symmetric matrices and positive definite matrices (real eigenvalues and orthogonal eigenvectors, tests for x'Ax > 0, applications) A=QLQT  Singular Value Decomposition (SVD)  The MoorePenrose Pseudoinverse. Least solution underdetermined system.
LU Factorisation Skewsymmetric matrices / skew matrices Fourier matrices / fast Fourier transform Graphs and networks Kronecker product 
Learning Outcomes 

On completion of this module the learner will/should be able to 

Assessment Strategies 

A terminal exam and continuous assessment will be used to assess the module. To reinforce the theoretical principles covered in lectures, learners will participate in project work. The learner will complete a final exam at the end of the semester. The learner is required to pass both the projects and terminal examination element of this module. 
Module Dependencies 

Pre Requisite Modules 
Co Requisite Modules 
Incompatible Modules 
Coursework Assessment Breakdown  % 

Course Work / Continuous Assessment  60 % 
End of Semester / Year Formal Examination  40 % 
Coursework Assessment Breakdown 

Description  Outcome Assessed  % of Total  Assessment Week 

CA 1  1,2,4  30  Week 6 
Project  1,2,3,4,5,6,7  30  Week 12 
End Exam Assessment Breakdown 

Description  Outcome Assessed  % of Total  Assessment Week 

Terminal Exam  1,2,3,4,5,6,7  40  End of Semester 
Mode Workload 

Type  Location  Description  Hours  Frequency  Avg Weekly Workload 

Lecture  Lecture Theatre  Lecture  2  Weekly  2.00 
Laboratory Practical  Computer Laboratory  Laboratory Practical  2  Fortnightly  1.00 
Independent Learning  Not Specified  Independent Learning  7  Weekly  7.00 
Total Average Weekly Learner Workload 3.00 Hours 

Mode Workload 

Type  Location  Description  Hours  Frequency  Avg Weekly Workload 

Total Average Weekly Learner Workload 0.00 Hours 

Mode Workload 

Type  Location  Description  Hours  Frequency  Avg Weekly Workload 

Total Average Weekly Learner Workload 0.00 Hours 

Mode Workload 

Type  Location  Description  Hours  Frequency  Avg Weekly Workload 

Lecture  Online  Theory Lecture  1  Weekly  1.00 
Independent Learning  Not Specified  Independent Learning  8.5  Weekly  8.50 
Laboratory Practical  Online  Online lab  0.5  Weekly  0.50 
Total Average Weekly Learner Workload 1.50 Hours 

Resources 

Book Resources 

Other Resources 
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Url Resources 
x 
Additional Info 
ISBN BookList 

Book Cover  Book Details 
Gilbert Strang 2016 Introduction to Linear Algebra WellesleyCambridge Press ISBN10 0980232775 ISBN13 9780980232776 

Gilbert Strang 2007 Computational Science and Engineering WellesleyCambridge Press ISBN10 0961408812 ISBN13 9780961408817 

Philip N Klein 2013 Coding the Matrix: Linear Algebra through Applications to Computer Science Newtonian Press ISBN10 0615880991 ISBN13 9780615880990 