# Describing Multi-dimensional Data

## Descriptions of Multidimensional Data

### Dispersion Matrix

As defined in Correlation Coefficient and Covariance for Numeric Data, covariance is about the variance of two series. This property makes it easy to generalize it to multidimensional data.

The generalized quantity is named as **dispersion matrix**. Suppose we have a $p$ dimensional dataset $X$,

index | $x_1$ | $x_2$ | … | $x_p$ |
---|---|---|---|---|

1 | 2.3 | 12.3 | 83.2 | 9.3 |

… | … | … | … | … |

N | 3.1 | 5.6 | 23.6 | 8.2 |

We could then calculate the pairwise covariance between the different dimensions.

$x_1$ | $x_2$ | … | $x_p$ | |
---|---|---|---|---|

$x_1$ | ||||

$x_2$ | ||||

… | ||||

$x_p$ |

Planted:
by L Ma;

Dynamic Backlinks:

L Ma (2018). 'Describing Multi-dimensional Data', Datumorphism, 12 April. Available at: https://datumorphism.leima.is/wiki/statistics/multidimensional-data/.