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B.Stat-106: Matrix Algebra
Course Code : B.Stat-106
Course Title : Matrix Algebra
Course Type : Related
Level/Term and Section : B.Sc. Honours Part – I
Academic Session : 2019 – 2020
Course Instructor : ×
Pre-requisite (If any) : ×
Credit Value : 4
Total Marks : 100 (Examination 80, Tutorial/Terminal 15, and Attendance 5)

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COURSE DESCRIPTION:
Matrix Algebra is a basic course in statistics with a strong application in the consecutive years. It aims to provide an overview of the relevant aspects with basic algebraic properties of matrices and to accustom with the fundamentals of vectors.
COURSE OBJECTIVES (CO):
1)
 Students will understand the concept of matrix and vectors.
2)
 Students will be prepared themselves for basic matrix operation.
3)
 Students able to solve the practical problems in matrix and vector.
4)
 Students will be able to apply matrix algebra in statistics as well as in any other field.
COURSE LEARNING OUTCOME (CLO):
On successful completion of the course
1)
 students will be able to know the fundamental the concepts of vector and its properties;
2)
 develop specific skills and competencies vector operations;
3)
 students will know the basic of matrices and matrix properties;
4)
 students will able to compute the characteristic roots and solution of system of equations;
5)
 quadratic forms, diagonalization and different decomposition should be known;
6)
 apply secured knowledge to solve problems in further statistical courses.
COURSE PLAN / SCHEDULE: 
CLO Topics to be covered
Teaching-Learning Strategies 
Assessment Techniques 
No. of Lectures
1
Introduction of Vectors: Definition of vector and plane, Vector space, Basis, Dimension, Sub-space.
 Lecturing with Multimedia Projector, Interactive Board and Q/A session Assignment, Class Tests, Presentation, Final Exam.
5
2
Plane and real line as geometric and algebraic vector spaces their relations, Linear dependence and independence, Dot product, Direct sum, Kronecker product, Projection, Gram-Schmidth orthogonalization, Cauchy-Schewartz inequality.
15
3
Matrices:  Definition and Basic operations, Types of matrices, Trace, Determinants, Rank, Inverse with their properties and applications, Inverse by partitioning,  Block matrices and their multiplication.
20
4
Solution of system of linear equations, Characteristic equations, Latent root and vector, Generalized inverse, Moore-Penrose inverse.
10
5
Quadratic forms and its geometric interpretations, Diagonalization, Spectral decomposition, LU and QR decompositions and its importance.
10
Assessment Strategy Evaluation Policy (Grading System) and make-up procedures: According to the ordinance.

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Main Books Recommended:
1) Basilevsky, A. (2013). Applied matrix algebra in the statistical sciences. Courier Dover Publications.
2) Eldén, L. (2009). Matrix Methods in Data Mining and Pattern Recognition. AMC, 10, 12.

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References:
3) Frank Jr, A. Y. R. E. S. (1996). Matrices. Colección Schaum. McGraw Hill.
4) Harville, D. A. (2008). Matrix algebra from a statistician’s perspective. Springer.
5) Lang, S. (2012). Introduction to linear algebra. Springer Science & Business Media.
6) Lipschutz, S., & M. Lipson (2001). Schaum’s outline of theory and problems of linear algebra. Erlangga.
7) Rao, C. R. (2009). Linear statistical inference and its applications (Vol. 22). John Wiley & Sons.
8) Searle, S. R., & Khuri, A. I. (2017). Matrix algebra useful for statistics. John Wiley & Sons.
9) Seber, G. A. (2008). A matrix handbook for statisticians. John Wiley & Sons.