MAT3004 Applied Linear Algebra L T P J C
3 2 0 0 4
Pre-requisite MAT2002 Applications of Differential and Syllabus Version
Difference Equations
1.1
Course Objectives
1. Understanding basic concepts of linear algebra to illustrate its power and utility through
applications to computer science and Engineering.
2. Apply the concepts of vector spaces, linear transformations, matrices and inner product
spaces in engineering.
3. Solve problems in cryptography, computer graphics and wavelet transforms
Course Outcomes
At the end of this course the students are expected to learn
1. the abstract concepts of matrices and system of linear equations using decomposition
methods
2. the basic notion of vector spaces and subspaces
3. apply the concept of vector spaces using linear transforms which is used in computer
graphics and inner product spaces
4. applications of inner product spaces in cryptography
5. Use of wavelet in image processing.
Student Learning Outcomes(SLO) 1,2,7
Module:1 System of Linear Equations 6 hours
Gaussian elimination and Gauss Jordan methods - Elementary matrices- permutation matrix -
inverse matrices - System of linear equations - - LU factorizations.
Module:2 Vector Spaces 6 hours
The Euclidean space and vector space- subspace –linear combination-span-linearly
dependent-independent- bases - dimensions-finite dimensional vector space.
Module:3 Subspace Properties 6 hours
Row and column spaces -Rank and nullity – Bases for subspace – invertibility- Application in
interpolation.
Module:4 Linear Transformations and applications 7 hours
Linear transformations – Basic properties-invertible linear transformation - matrices of linear
transformations - vector space of linear transformations – change of bases – similarity
Module:5 Inner Product Spaces 6 hours
Dot products and inner products – the lengths and angles of vectors – matrix representations of
inner products- Gram-Schmidt orthogonalisation
Module:6 Applications of Inner Product Spaces: 6 hours
,QR factorization- Projection - orthogonal projections – relations of fundamental subspaces –
Least Square solutions in Computer Codes
Module:7 Applications of Linear equations : 6 hours
An Introduction to coding - Classical Cryptosystems –Plain Text, Cipher Text, Encryption,
Decryption and Introduction to Wavelets (only approx. of Wavelet from Raw data)
Module:8 Contemporary Issues: 2 hours
Industry Expert Lecture
Total lecture hours: 45 hours
Tutorial • A minimum of 10 problems to be worked out by 30 hours
students in every Tutorial Class
• Another 5 problems per Tutorial Class to be given as
home work.
Text Book(s)
1. Linear Algebra, Jin Ho Kwak and Sungpyo Hong, Second edition Springer(2004).
(Topics in the Chapters 1,3,4 &5)
2. Introductory Linear Algebra- An applied first course, Bernard Kolman and David, R.
Hill, 9th Edition Pearson Education, 2011.
Reference Books
1. Elementary Linear Algebra, Stephen Andrilli and David Hecker, 5th Edition,
Academic Press(2016)
2. Applied Abstract Algebra, Rudolf Lidl, GuterPilz, 2 nd Edition, Springer 2004.
3. Contemporary linear algebra, Howard Anton, Robert C Busby, Wiley 2003
4. Introduction to Linear Algebra, Gilbert Strang, 5 th Edition, Cengage Learning (2015).
Mode of Evaluation: Digital Assignments, Continuous Assessments, Final Assessment Test
Recommended by Board of Studies 25-02-2017
Approved by Academic Council No. 47 Date 05-10-2017
,In one of the triannual SIAM conferences on applied linear algebra, a dive
of internationally recognized scientific corporations and government la
was asked how linear algebra finds application in their missions.
The overwhelming response was that the primary use of linear algebra i
industrial and laboratory work involves the development, analy
implementation of numerical algorithms along with some discrete and
modelling.
, ▪ Image Processing
▪ Flow in a network of pipes
▪ Current and voltage in LCR circuits
▪ Cryptography
▪ Machine learning (Support Vector Machine, Principle Component Analysis)
▪ Load and displacements in structures
▪ Finite element analysis (has Mechanical, Electrical, and Thermodynamic
applications)
▪ Many more…
3 2 0 0 4
Pre-requisite MAT2002 Applications of Differential and Syllabus Version
Difference Equations
1.1
Course Objectives
1. Understanding basic concepts of linear algebra to illustrate its power and utility through
applications to computer science and Engineering.
2. Apply the concepts of vector spaces, linear transformations, matrices and inner product
spaces in engineering.
3. Solve problems in cryptography, computer graphics and wavelet transforms
Course Outcomes
At the end of this course the students are expected to learn
1. the abstract concepts of matrices and system of linear equations using decomposition
methods
2. the basic notion of vector spaces and subspaces
3. apply the concept of vector spaces using linear transforms which is used in computer
graphics and inner product spaces
4. applications of inner product spaces in cryptography
5. Use of wavelet in image processing.
Student Learning Outcomes(SLO) 1,2,7
Module:1 System of Linear Equations 6 hours
Gaussian elimination and Gauss Jordan methods - Elementary matrices- permutation matrix -
inverse matrices - System of linear equations - - LU factorizations.
Module:2 Vector Spaces 6 hours
The Euclidean space and vector space- subspace –linear combination-span-linearly
dependent-independent- bases - dimensions-finite dimensional vector space.
Module:3 Subspace Properties 6 hours
Row and column spaces -Rank and nullity – Bases for subspace – invertibility- Application in
interpolation.
Module:4 Linear Transformations and applications 7 hours
Linear transformations – Basic properties-invertible linear transformation - matrices of linear
transformations - vector space of linear transformations – change of bases – similarity
Module:5 Inner Product Spaces 6 hours
Dot products and inner products – the lengths and angles of vectors – matrix representations of
inner products- Gram-Schmidt orthogonalisation
Module:6 Applications of Inner Product Spaces: 6 hours
,QR factorization- Projection - orthogonal projections – relations of fundamental subspaces –
Least Square solutions in Computer Codes
Module:7 Applications of Linear equations : 6 hours
An Introduction to coding - Classical Cryptosystems –Plain Text, Cipher Text, Encryption,
Decryption and Introduction to Wavelets (only approx. of Wavelet from Raw data)
Module:8 Contemporary Issues: 2 hours
Industry Expert Lecture
Total lecture hours: 45 hours
Tutorial • A minimum of 10 problems to be worked out by 30 hours
students in every Tutorial Class
• Another 5 problems per Tutorial Class to be given as
home work.
Text Book(s)
1. Linear Algebra, Jin Ho Kwak and Sungpyo Hong, Second edition Springer(2004).
(Topics in the Chapters 1,3,4 &5)
2. Introductory Linear Algebra- An applied first course, Bernard Kolman and David, R.
Hill, 9th Edition Pearson Education, 2011.
Reference Books
1. Elementary Linear Algebra, Stephen Andrilli and David Hecker, 5th Edition,
Academic Press(2016)
2. Applied Abstract Algebra, Rudolf Lidl, GuterPilz, 2 nd Edition, Springer 2004.
3. Contemporary linear algebra, Howard Anton, Robert C Busby, Wiley 2003
4. Introduction to Linear Algebra, Gilbert Strang, 5 th Edition, Cengage Learning (2015).
Mode of Evaluation: Digital Assignments, Continuous Assessments, Final Assessment Test
Recommended by Board of Studies 25-02-2017
Approved by Academic Council No. 47 Date 05-10-2017
,In one of the triannual SIAM conferences on applied linear algebra, a dive
of internationally recognized scientific corporations and government la
was asked how linear algebra finds application in their missions.
The overwhelming response was that the primary use of linear algebra i
industrial and laboratory work involves the development, analy
implementation of numerical algorithms along with some discrete and
modelling.
, ▪ Image Processing
▪ Flow in a network of pipes
▪ Current and voltage in LCR circuits
▪ Cryptography
▪ Machine learning (Support Vector Machine, Principle Component Analysis)
▪ Load and displacements in structures
▪ Finite element analysis (has Mechanical, Electrical, and Thermodynamic
applications)
▪ Many more…
