Unit No | Topics |
---|---|

1 |
Review of algebra of matrices & elementary transformations, Rank of a matrix, inverse of a matrix by Gauss-Jordan method, normal form of a matrix, Solution of system of algebraic simultaneous equations, Linear dependent and Linear independent vectors. Eigen values and Eigen vectors, Eigen values and Eigen vectors of: Symmetric, Skewsymmetric, Hermitian, Skewhermitian, Unitary and Normal matrix, Algebraic and Geometric multiplicity, Diagonalization, Spectral theorem for real symmetric matrices, Application of Quadratic forms. |

2 |
Vectors in R |

3 |
Definition and basic properties, Types of linear transformation(Rotation,reflection,expansion,contraction,shear,projection),Matrix of linear transformations,Change of basis and similarity, Rank nullity theorem |

4 |
Definition, Comparison test, Cauchy’s integral test, ratio test, root test, Leibniz’s rule for alternating series, power series, range of convergence, uniform convergence. |

Attachment | Size |
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Linear Algebra.pdf | 173.62 KB |