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Course Detail

Course Name Linear Algebra
Course Code 24MAT116
Program Integrated M. Sc. Mathematics and Computing
Semester II
Credits 4
Campus Coimbatore

Summary

Vector Spaces: Vector spaces – Sub spaces – Linear independence – Basis – Dimension.

Inner Product Spaces: Inner products – Orthogonality – Orthogonal basis – Gram Schmidt Process – Change of basis – Orthogonal complements – Projection on subspace – Least Square Principle.

Linear Transformations: Positive definite matrices – Matrix norm and condition number – QR- Decomposition – Linear transformation – Relation between matrices and linear transformations – Kernel and range of a linear transformation – Change of basis – Nilpotent transformations – Trace and Transpose, Determinants, Symmetric and Skew Symmetric Matrices, Adjoint and Hermitian Adjoint of a Matrix, Hermitian, Unitary and Normal Transformations, Self Adjoint and Normal Transformations, Real Quadratic Forms.

Eigen values and Eigen vectors: Problems in Eigen Values and Eigen Vectors, Diagonalization, Orthogonal Diagonalization, Quadratic Forms, Diagonalizing Quadratic Forms, Conic Sections. Similarity of linear transformations – Diagonalisation and its applications – Jordan form and rational canonical form.

Text Book & References

Text Book

1.Howard Anton and Chris Rorres, “Elementary Linear Algebra”, Tenth Edition, John Wiley & Sons, 2010.

References

a) Nabil Nassif, Jocelyne Erhel, Bernard Philippe, Introduction to Computational Linear Algebra, CRC press, 2015.
b) Sheldon Axler, Linear Algebra Done Right, Springer, 2014.
c) Gilbert Strang, “Linear Algebra for Learning Data”, Cambridge press, 2019. d) Kenneth Hoffmann and Ray Kunze, Linear Algebra, Second Edition, Prentice Hall, 1971. e) Mike Cohen, Practical Linear Algebra for Data Science, Oreilly Publisher, 2022.

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