skewsymmetry {asymmetry} | R Documentation |

## Decompose an Asymmetric Matrix into Symmetric and Skew-symmetric Components

### Description

The decomposition of an asymmetric matrix into a symmetric matrix and a skew-symmetric matrix is an elementary result from mathematics that is the cornerstone of this package. The decomposition into a skew-symmetric and a symmetric component is written as: `Q=S+A`

, where `Q`

is an asymmetric matrix, `S`

is a symmetric matrix, and `A`

is a skew-symmetric matrix. This decomposition provides a justification for separate analyses of `S`

and `A`

. This decomposition is a useful tool for data analysis and graphical representation by areas. A second application is to the study of an asymmetric matrix of residuals, obtained after fitting a MDS model.

### Usage

```
skewsymmetry(x)
```

### Arguments

`x` |
Asymmetric matrix |

### Value

`S` |
The symmetric part of the matrix |

`A` |
The skew-symmetric part of the matrix |

`linear` |
The row means of the skew-symmetric matrix, this amounts to fitting a linear model with row and column effects to the skew-symmetric matrix |

`sv` |
The singular vectors of the skew-symmetric matrix |

`sval` |
a vector containing the singular values of the skew-symmetric part of the data matrix |

`nobj` |
The number of objects |

### See Also

### Examples

```
data("Englishtowns")
Q <- skewsymmetry(Englishtowns)
# the skew-symmetric part
Q$A
```

*asymmetry*version 2.0.4 Index]