'Linear Algebra' is a course offered for the of B. Tech. programs at the School of Engineering, Amrita Vishwa Vidyapeetham.
Unit 1
Vector Spaces: Vector spaces - Sub spaces - Linear independence - Basis - Dimension - Inner products - Orthogonality - Orthogonal basis - Gram Schmidt Process.
Unit 2
Change of basis - Orthogonal complements - Projection on subspace - Least Square Principle. Linear Transformations: Positive definite matrices - Matrix norm and condition number – QR - Decomposition
Unit 3
Linear transformation - Relation between matrices and linear transformations - Kernel and range of a linear transformation - Change of basis - Nilpotent transformations - Similarity of linear transformations - Diagonalisation and its applications - Jordan form and rational canonical form.
- Howard Anton and Chris Rorres, “Elementary Linear Algebra”, Tenth Edition, John Wiley & Sons, 2010.
- Gilbert Strang, “Linear Algebra and Its Applications”, Fourth Edition, Cengage, 2006.
- Kenneth Hoffmann and Ray Kunze, Linear Algebra, Second Edition, Prentice Hall, 1971.
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