# vectorization of matrix

The vectorization of a $m\times n$ matrix $A=({a}_{ij})$ the matrix to a column vector^{} $\text{vec}(A)$, which consists of all columns of $A$ stacked in :

$$\text{vec}(A):={\left({a}_{11}{a}_{21}\mathrm{\dots}{a}_{m1}{a}_{12}{a}_{22}\mathrm{\dots}{a}_{m2}\mathrm{\dots}\mathrm{\dots}{a}_{1n}{a}_{2n}\mathrm{\dots}{a}_{mn}\right)}^{\u22ba}$$ |

The mapping vec from the vector space^{} formed by the $m\times n$ matrices to the vector space of the column vectors of the $mn$ is apparently a linear transformation.

Title | vectorization of matrix |
---|---|

Canonical name | VectorizationOfMatrix |

Date of creation | 2013-03-22 18:12:20 |

Last modified on | 2013-03-22 18:12:20 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 4 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 15-01 |

Synonym | vectorization |

Synonym | vectorisation |

Related topic | transpose^{} |