## Linear Algebra Assignment Help

Linear Algebra is a study of vector spaces and the linear mapping between these spaces. It is a study of lines, planes, subspaces and Vector spaces. Linear Algebra study deals with vector spaces (associativity, commutativity, inverse elements, identity elements etc.), linear transformations (Kernel and Range Theorem, Inverse transformations, Change of Base, Representative Matrix), Eigenvalues and eigenvectors, Matrix theory, subspaces, Inner products spaces (Inner Product, Euclidean Space, Gram-Smith, Orthogonality, Hilbert Spaces) and determinants. Some of the applications of Linear Algebra are solution of linear systems, least-squares best fit line, Quantum mechanics and Fourier series expansion.

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Linear Spaces | Subspaces |

Linear Dependence and Linear Independence | Isomorphisms and invertibility |

Quotient Spaces | Dual Spaces |

Linear algebra and differential equations | Linear Mappings |

Orthogonal bases and orthogonal projections | Linear transformations |

Algebra of Linear Maps | Gram-Schmidt process |

Similarity Transformations | Gauss - Seidel method |

Matrices - Matrix Representation of Linear Maps, Matrix Inverse, Matrix Multiplication | Determinant |

Gaussian Elimination | Laplace Expansion |

Cramer's Rule | Matrix analysis and applied linear algebra |

Eigenvalues and Eigenvectors | Cayley-Hamilton Theorem |

Diagonalization | Euclidean vectors |