# Linear Algebra/Notation

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### Notation[edit]

, , | set of real numbers, reals greater than , ordered -tuples of reals |

natural numbers: | |

complex numbers | |

set of . . . such that . . . | |

, |
interval (open or closed) of reals between and |

sequence; like a set but order matters | |

vector spaces | |

vectors | |

, |
zero vector, zero vector of |

bases | |

standard basis for | |

basis vectors | |

matrix representing the vector | |

set of -th degree polynomials | |

set of matrices | |

span of the set | |

direct sum of subspaces | |

isomorphic spaces | |

homomorphisms, linear maps | |

matrices | |

transformations; maps from a space to itself | |

square matrices | |

matrix representing the map | |

matrix entry from row , column | |

determinant of the matrix | |

rangespace and nullspace of the map | |

generalized rangespace and nullspace |

### Lower case Greek alphabet[edit]

**About the Cover.** This is Cramer's Rule for the system , . The size of the first box is the determinant shown (the absolute value of the size is the area). The size of the second box is times that, and equals the size of the final box. Hence, is the final determinant divided by the first determinant.