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• 7:17 PM, Monday, 18 Oct 2021

 Course Postgraduate Semester Sem. I Subject Code AVC611 Subject Title Mathematics for Control

##### Syllabus

Matrix Operations, Geometry of linear equations, Gaussian elimination, Triangular  , Inverses and Transposes.

Vector Spaces: Linear independence, Basis ,Dimension, Four fundamental subspaces, Linear transformations.

Orthogonality: Orthogonal vectors, orthogonality, normed vector spaces.

Least squares: Orthogonal projections and least squares fitting, applications to data analysis Orthogonilization and orthonormalization: the Gram‐Schimddt process, linear functional, dual spaces and dual bases.

Determinants: Determinant calculation, relation to linear transformations.

Eigenvalues and eigenvectors: Definition, significance, calculation of eigenvalues and eigenvectors.

Similarity of matrices: Definition, properties, and consequences of similarity; invariants under similarity transformation; similarity classes. Congruence transformations, diagonalization and invariants: Invariants of congruence, reduction to congruence Normal Form”.

Introduction to Probablity and Random Variables: distribution functions, binomial, geometric, hypergeometric, and Poisson distributions, uniform, exponential, normal, gamma and beta

distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

##### Text Books
1. Gilbert Strang ,Linear Algebra and its Applications, 4th ed., Thomson Learning Co., Belmont CA, 2006.
2. Kenneth Hoffman and Ray Kunze, Linear Algebra, 2nd ed., , Prentice‐ Hall 1971.
3. Roger Horn and Charles Johnson, Matrix analysis, Cambridge University Press, 1990.
4. Athanasios Papoulis, Probability, Random Variables and Stochastic Processes,McGraw‐Hill Science, 2001.
5. David S. Watkins, Fundamentals of Matrix Computations, Wiley Interscience, 2002.
6. Gene H. Golub, Charles F. Van Loan, Matrix Computations, JHU Press, 1996.
7. Ross, Sheldon, A First Course in Probability. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2009.
##### References

Same as Textbooks