## Details of MA2102 (Autumn 2016)

Level: 2 |
Type: Theory |
Credits: 3.0 |

Course Code | Course Name | Instructor(s) |
---|---|---|

MA2102 |
Linear Algebra |
Shibananda Biswas |

Syllabus |
---|

MA2102 Linear Algebra (3 Credits)
Vector Spaces: Definition of a vector space, examples, linear independence, basis and dimension; scalar product, orthogonal basis and the Gram-Schmidt orthogonalization process. Linear Operators: Definition, matrix representation of linear operators, rank of a matrix, determinants, nonsingularity, partitioned matrices, special types of matrices; change of basis. Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors of a matrix, the characteristic polynomial, diagonalization. Similarity: Orthogonal, unitary and Hermitian matrices, unitary similarity, Schur's triangularization theorem, the spectral theorem for normal matrices; the QR algorithm; the Hermite normal form, the Jordan canonical form and the minimal polynomial. |

References |
---|

Suggested Texts / Reference Books:
1. Axler, S., Linear Algebra Done Right (2nd Edition), Undergraduate Texts in Mathematics, Springer-Verlag, 1997. 2. Horn, R. and Johnson, C. R., Matrix Analysis, Cambridge University Press, 1985. 3. Hoffman, K. and Kunze, R., Linear Algebra (2nd Edition), Prentice-Hall, 1971. 4. Lang, S., Introduction to Linear Algebra (2nd Edition), Springer-Verlag, 1997. 5. Rao, A. R. and Bhimasankaram, P., Linear Algebra (2nd Edition), Texts and Readings in Mathematics, Hindustan Book Agency, 2000. |

#### Course Credit Options

Sl. No. | Programme | Semester No | Course Choice |
---|---|---|---|

1 | IP | 1 | Not Allowed |

2 | IP | 3 | Not Allowed |

3 | IP | 5 | Not Allowed |

4 | MR | 1 | Not Allowed |

5 | MR | 3 | Not Allowed |

6 | MS | 3 | Core |

7 | RS | 1 | Not Allowed |

8 | RS | 2 | Not Allowed |