Week | Subjects to be covered |
---|---|

1 | Matrices, operations on matrices, special types of matrices . |

2 | Elementary row operations, row equivalence . |

3 | Invertibility, inverse of a matrix , Systems of linear equations . |

4 | Gaussian Elimination, Homogeneous equations, invertibility and systems . |

5 | Determinants: definition, properties. |

6 | Cofactor expansion, Cramer’s rule, Trace. |

7 | Vector Spaces, subspaces, linear span, linear independence. |

8 | Basis and dimension, coordinates, row space, column space, solution space of a matrix. |

9 | Inner product spaces, norm and orthogonality |

10 | Orthogonal and orthonormal bases, the Gram-Schmidt orthogonalization process, orthogonal projections |

11 | Eigenvalues, eigenvectors and diagonalization |

12 | Matrix exponentials, diagonalization of real symmetric matrices |

13 | Linear transformations, Kernel and image. |

14 | Matrix representation of linear transformations |