A D102: Matrix $y : J \times I \to X$ is a

**transpose**of $x$ if and only if \begin{equation} \forall \, j \in J : \forall \, i \in I : y_{j, i} = x_{i, j} \end{equation}

▼ | Set of symbols |

▼ | Alphabet |

▼ | Deduction system |

▼ | Theory |

▼ | Zermelo-Fraenkel set theory |

▼ | Set |

▼ | Binary cartesian set product |

▼ | Binary relation |

▼ | Map |

▼ | Countable map |

▼ | Array |

▼ | Matrix |

Definition D398

Matrix transpose

Formulation 0

Let $x : I \times J \to X$ be a D102: Matrix.

A D102: Matrix $y : J \times I \to X$ is a**transpose** of $x$ if and only if
\begin{equation}
\forall \, j \in J :
\forall \, i \in I :
y_{j, i} = x_{i, j}
\end{equation}

A D102: Matrix $y : J \times I \to X$ is a

Children

▶ | Complex matrix antisymmetric part |

▶ | Complex matrix symmetric part |

▶ | Symmetric matrix |

Results