Linear Algebra

Course Title: Linear Algebra

Course No: BDS155

Nature of the Course: THEORY

Semester: 2

Full Marks: 45 + 30

Pass Marks: 18 + 12

Credit Hours: 3

Course Description

This course emphasizing topics useful in other disciplines covers fundamental algebraic tools involving matrices and vectors to study linear systems of equations and linear transformations, eigenvalues and eigenvectors and their wide range of applications.

Course Objectives

After successful completion of this course the student will be able to

use matrix and determinants to solve various mathematical and real life problems.
acquire knowledge of vectors spaces and linear transformations.
apply eigenvalues and eigenvectors in solving various problems.

Course Contents

1. Matrix and Determinants

10 hrs

1.1. Algebra of matrices

1.2. Determinants and its properties

1.3. Application of determinants

1.4. Complex matrices

1.5. Rank of matrices

1.6. System of linear equations and its matrix form

1.7. Row reduction and echelon forms

1.8. LU factorization

2. Vectors Spaces

12 hrs

2.1. Points in n-space

2.2. Algebra of points in n-space

2.3. Scalar and dot product

2.4. Norm and its properties

2.5. Distance

2.6. Angle between two vectors

2.7. Orthogonality

2.8. Scalar and vector projections

2.9. Cosines of lines

2.10. Projections

2.11. Vector spaces and subspaces

2.12. Linear combination, dependence and independence

2.13. Span, basis and dimension

3. Linear Transformations

8 hrs

3.1. Linear transformations

3.2. Kernel and image

3.3. Algebra of linear transformations

3.4. Matrix representation of a linear transformations

3.5. Four fundamental subspaces

3.6. Applications to difference equations

3.7. Applications to Markov chains

4. Orthogonality

8 hrs

4.1. Orthogonal vectors and sets

4.2. Orthogonal bases and Gram-Schmidt Process

4.3. QR-factorization

4.4. Least squares method

5. Eigenvalues and Eigenvectors

10 hrs

5.1. Eigenvalues and Eigenvectors

5.2. Cayley-Hamilton theorem and its application

5.3. Eigenvalue decomposition

5.4. Diagonalization of a matrix

5.5. Difference equations and powers A^k

5.6. Singular value decomposition

Reference Books

1.David C. Lay, Linear Algebra and its Applications, Pearson Education, 2012.
2.Gilbert Strang, Introduction to Linear Algebra, 4th Edition, Wellesley-Cambridge Press.
3.Howard Anton, Chris Rorres, Elementary Linear Algebra: Applications Version, Wiley, 2014.

Notes:

This syllabus follows the official BDS curriculum of Tribhuvan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.

Linear Algebra

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Linear Algebra

Course Description

Course Objectives

Course Contents

Reference Books

Notes: