'Matrix Algebra' is a course offered in the first semester of  B. Tech. programs at the School of Engineering, Amrita Vishwa Vidyapeetham.

Course Outcomes

CO1: Understand the notion of eigenvalues and eigenvectors, analyze the possibility of diagonalization and hence compute a diagonal matrix, if possible.

CO2: Apply the knowledge of diagonalization to transform the given quadratic form into the principal axes form and analyze the given conic section.

CO3: Understand the advantages of the iterative techniques and apply it to solve the system of equations and finding eigenvectors.

Mapping of course outcomes with program outcomes:

  PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
CO1 3 2 1                  
CO2 2 3 1                  
CO3 3   1                  
CO4                        
CO5                        
CO6                        

Review: System of linear Equations, linear independence. (3 hrs)

Eigen values and Eigen vectors: Definitions and properties. Positive definite, negative definite and indefinite. (8 hrs) Diagonalization and Orthogonal Diagonalization. Properties of Matrices. Symmetric and Skew Symmetric Matrices, Hermitian and Skew Hermitian Matrices and Orthogonal matrices. (Sections: 8.1-8.4) (10 hrs)

Numerical Computations: L U factorization, Gauss Seidal and Gauss Jacobi methods for solving system of equations. Power Method for Eigen Values and Eigen Vectors. (Sections: 20.2, 20.3, 20.8) (8 hrs)

Evaluation Pattern:

Test-1 -25 marks (one hour test) after 15th lecture.

CA - 25 marks (Quizzes / assignments / lab practice) Test – 2- 50 marks (two-hour test) at the end of 30th lecture. Total - 100 marks.

Supplementary exam for this course will be conducted as a two-hour test for 100 marks.

Text Book:

  1. Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Tenth Edition, 2018.

Reference Books:

  1. Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.
  2. ‘Engineering Mathematics’, Srimanta Pal and Subhodh C Bhunia, John Wiley and Sons, 2012, Ninth Edition.