LINEAR ALGEBRA (BCS405D)

LINEAR ALGEBRA

Course Code BCS405D 
CIE Marks 50
Teaching Hours/Week (L:T:P:S) 2:2:0:0 
SEE Marks 50
Total Hours of Pedagogy 40 
Total Marks 100
Credits 03 
Exam Hours 03
Examination type (SEE) Theory

Module-1: VECTOR SPACES

Introduction, Vector spaces, Subspaces, Linear Combinations, Linear Spans, row space

and column space of a Matrix, Linear Dependence and Independence, Basis and

Dimension, Coordinates. (8 hours)

(RBT Levels: L1, L2 and L3)

Module-2: LINEAR TRANSFORMATIONS

Introduction, Linear Mappings, Geometric linear transformation of i2, Kernel and Image

of a linear transformations, Rank-Nullity Theorem (No proof), Matrix representation of

linear transformations, Singular and Non-singular linear transformations, Invertible

linear transformations

Module-3: EIGENVALUES AND EIGENVECTORS

Introduction, Polynomials of Matrices, Applications of Cayley-Hamilton Theorem, Eigen

spaces of a linear transformation, Characteristic and Minimal Polynomials of Block

Matrices, Jordan Canonical form. 

Module-4: INNER PRODUCT SPACES

Inner products, inner product spaces, length and orthogonality, orthogonal sets and

Bases, projections, Gram-Schmidt process, QR-factorization, least squares problem and

least square error.

Module-5: OPTIMIZATION TECHNIQUES IN LINEAR ALGEBRA

Diagonalization and Orthogonal diagonalization of real symmetric matrices, quadratic

forms and its classifications, Hessian Matrix, Method of steepest descent, Singular value

decomposition. Dimensionality reduction – Principal component analysis.

Suggested Learning Resources:

Text Books:

1. David C. Lay, Steven R. Lay, Judi J Mc. Donald: “Linear Algebra and its

applications”, Pearson Education, 6th Edition, 2021.

2. Gilbert Strang: “Linear Algebra and its applications”, Brooks Cole, 4th edition,

2005.

Reference Books:

1. Richard Bronson & Gabriel B. Costa: “Linear Algebra: An Introduction”, 2nd

edition. Academic Press, 2014.

2. Seymour Lipschutz, Marc Lipso: “Theory and problems of linear algebra”,

Schaum’s outline series - 6th edition, 2017, McGraw-Hill Education.

3. Marc Peter Deisennroth, A. Aldo Faisal, Cheng Soon Ong: “Mathematics for

Machine learning”, Cambridge University Press, 2020.

Web links and Video Lectures (e-Resources):

• https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall2011/index.htm

• https://www.math.ucdavis.edu/~linear/linear.pdf

• https://www.coursera.org/learn/linear-algebra-machine-learning

• https://nptel.ac.in/syllabus/111106051/

• http://nptel.ac.in/courses.php?disciplineID=111

• http://www.class-central.com/subject/math(MOOCs)

• http://academicearth.org/

• VTU e-Shikshana Program