Matrices for Engineers

MA25C10:

Matrices for Engineers

Course Objectives: The Objectives of the course are to enable the students to understand and apply matrix concepts such as eigenvalues, orthogonal transformations, matrix decompositions (QR and SVD), quadratic forms and least- squares solutions for solving engineering problems.

Matrices: Introduction – Characteristic equation – Eigenvalues and Eigenvectors of a real matrix – Properties of Eigen values and Eigen vectors (without proof) – Cayley – Hamilton theorem (Statement and applications only) - Orthogonal matrices – Orthogonal transformation of a symmetric matrix to diagonal form – Quadratic form – Nature of Quadratic forms - Reduction of quadratic form to canonical form by orthogonal transformation. Matrix norms, Jordan Normal form, QR decomposition – Singular Value Decomposition (SVD) - Least squares solutions- simple problems.

Activities: Computation of eigenvalues and eigenvectors, matrix norm, QR decomposition and SVD using open-source software, Solving Competitive Examination questions.

Weightage: Continuous Assessment: 40%, End Semester Examinations: 60%.

Assessment Methodology: Assignments (20%), Solution to application-oriented

problems using software (20%), Solving Competitive Examination questions (20%), Internal Examinations (40%).

References:

1. Erwin Kreyszig, Advanced Engineering Mathematics, (11th ed.), John Wiley & Sons, USA,2025.

2. Alan Jeffrey, Matrix Operations for Engineers and Scientists, Springer Science, 2010.

3. Gilbert Strang. Linear Algebra for Everyone. 2020. Wellesley-Cambridge Press