Course Code | MA 106 |

Course Name | Linear Algebra |

Offered to | UG/PG |

Pre-requisites | NIL |

Lecture | 3 |

Tutorial | 1 |

Practical | 0 |

Credit | 4* |

Reference | 1. H. Anton, Elementary linear algebra with applications (8th Edition), John Wiley (1995). 2. G. Strang, Linear algebra and its applications (4th Edition), Thom- son (2006). 3. S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India (2000). 4. E. Kreyszig, Advanced engineering mathematics (8th Edition), John Wiley (1999). |

Description | Vectors in Rn, notion of linear independence and dependence, linear span of a set of vectors, vector subspaces of Rn, basis of a vector subspace. Systems of linear equations, matrices and Gauss elimination, row space, null space, and column space, rank of a matrix. Determinants and rank of a matrix in terms of determinants. Abstract vector spaces, linear transformations, matrix of a linear trans-formation, change of basis and similarity, rank-nullity theorem. Inner pro duct spaces, Gram-Schmidt pro cess, orthonormal bases, pro-jections and least squares approximation. Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues of special matrices (orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal). algebraic and geometric multiplicity, diagonaliza-tion by similarity transformations, spectral theorem for real symmetric matrices, application to quadratic forms. |