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This is a branch of mathematics that deals with vectors along with the other key factors that insert one vector into another to generate an output based on the rules. This would deal with planes, subspaces, and lines. This is applied to pure and core mathematics. The algebra concept will be helping to solve various problems in matrices, algebra structures, and polynomials.

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Linear transformation | Subspaces |

Vector space | Span and basis |

Quotient spaces | Dual spaces |

Linear independence and dependence | Matrix theory |

Inner product space | Euclidean vectors |

Theorems of linear algebra | Linear maps |

Eigenvalues and vectors | Cramer's rule |

Isomorphism | 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 |

Matrices - Matrix Representation of Linear Maps, Matrix Inverse, Matrix Multiplication | Gauss-Seidel method |

Determinant | Gaussian Elimination |

Laplace Expansion | Cramer's Rule |

Matrix analysis and applied linear algebra | Eigenvalues and Eigenvectors |

Cayley-Hamilton Theorem | Diagonalization |

Euclidean vectors | Sigma Algebra |

Polynomials | Algebraic Geometry |