Unit I
Vector Spaces: Vector spaces – Sub spaces – Linear independence – Basis – Dimension.
Programs
- M. Tech. in Automotive Engineering -Postgraduate
- Fellowship in Cleft and Craniofacial Orthodontics 6 Months / 1 Year -Fellowship
| Course Name | Linear Algebra |
| Course Code | 24ASD503 |
| Program | M.Sc. in Applied Statistics and Data Analytics |
| Semester | 1 |
| Credits | 4 |
| Campus | Coimbatore , Kochi |
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 – – Linear transformation – Relation between matrices and linear transformations – Kernel and range of a linear transformation – Trace and Transpose, Determinants, Symmetric and Skew Symmetric Matrices.
Eigen values and Eigen vectors: Problems in Eigen Values and Eigen Vectors, Diagonalization, Orthogonal Diagonalization, Quadratic Forms, Diagonalizing Quadratic Forms.
Decomposition of matrices: LU, QR and SVD
Course Outcomes:
CO-1: To understand the axioms in the definition of a vector space through examples; to understand Subspaces, basis and its relevance.
CO-2: To understand inner products and compute the angle/length of a vector and the orthonormal basis.
CO-3: To understand the concepts of Linear Transformations and Matrices for Linear Transformation
CO-4: To understand the concepts of Eigen Values, Eigen Vectors & Diagonalization form.
CO-5: Decompositions : LU,QR and SVD
CO-PO Mapping:
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Text Books / Reference Books:
1) Howard Anton and Chris Rorres, “Elementary Linear Algebra”, 10th Edition, John Wiley
& Sons, 2010.
2) Linear Algebra, Arnold J. Insel, Lawrence E. Spence, and Stephen H. Friedberg, 5th
Edition, Pearson Education, 2014.
3) Nabil Nassif, Jocelyne Erhel, Bernard Philippe, Introduction to Computational Linear
Algebra, CRC press, 2015.
4) Sheldon Axler, Linear Algebra Done Right, Springer, 2014.
5) Gilbert Strang, “Linear Algebra for Learning Data”, Cambridge press, 2019.
6) Kenneth Hoffmann and Ray Kunze, Linear Algebra, Second Edition, Prentice Hall, 1971.
7) Mike Cohen, Practical Linear Algebra for Data Science, Oreilly Publisher, 2022.
8) I. N. Herstein, ‘Topics in Algebra’, Second Edition, John Wiley and Sons, 2000.
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