The function constructs the extended full-block multiplier

Here the inputs should satisfy the following constraints:

- with and
- with and
- denotes the number of positive eigenvalues of (this equals the size of )
- denotes the number of negative eigenvalues of (this equals the size of )
- specifies the type of extention:
- :
- :

- :

Let and . Then the different types are defined as follows:

Type | Description |

type=1 | Define and let where is the collection of eigenvectors corresponding to the positive eigenvalues of and is the collection of eigenvectors corresponding to the negative eigenvalues of . Then . |

type=2 | Define and let where is the collection of eigenvectors corresponding to the positive eigenvalues of and is the collection of eigenvectors corresponding to the negative eigenvalues of . Then . |

type=3 | – Factorize and with and respectively and define and – Define with begin the singular value decomposition. Also denote by and – Let where and respectively denote the collection of eigenvectors corresponding to the positive and negative eigenvalues of Then |

type=4 | Define and let where is the collection of eigenvectors corresponding to the positive eigenvalues of and is the collection of eigenvectors corresponding to the negative eigenvalues of . Then . |

type=5 | Define and let where is the collection of eigenvectors corresponding to the positive eigenvalues of and is the collection of eigenvectors corresponding to the negative eigenvalues of . Then . |

type=6 | – Factorize and with and respectively and define and – Define with begin the singular value decomposition. Also denote by and – Let where and respectively denote the collection of eigenvectors corresponding to the positive and negative eigenvalues of Then |