A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices
The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of wh...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/4590817 |
| id |
doaj-8462e325f45b4c5c829714424287260d |
|---|---|
| record_format |
Article |
| spelling |
doaj-8462e325f45b4c5c829714424287260d2020-11-24T21:18:30ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422016-01-01201610.1155/2016/45908174590817A Note on the vec Operator Applied to Unbalanced Block-Structured MatricesHal Caswell0Silke F. van Daalen1Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, NetherlandsInstitute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, NetherlandsThe vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes.http://dx.doi.org/10.1155/2016/4590817 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hal Caswell Silke F. van Daalen |
| spellingShingle |
Hal Caswell Silke F. van Daalen A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices Journal of Applied Mathematics |
| author_facet |
Hal Caswell Silke F. van Daalen |
| author_sort |
Hal Caswell |
| title |
A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices |
| title_short |
A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices |
| title_full |
A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices |
| title_fullStr |
A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices |
| title_full_unstemmed |
A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices |
| title_sort |
note on the vec operator applied to unbalanced block-structured matrices |
| publisher |
Hindawi Limited |
| series |
Journal of Applied Mathematics |
| issn |
1110-757X 1687-0042 |
| publishDate |
2016-01-01 |
| description |
The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes. |
| url |
http://dx.doi.org/10.1155/2016/4590817 |
| work_keys_str_mv |
AT halcaswell anoteonthevecoperatorappliedtounbalancedblockstructuredmatrices AT silkefvandaalen anoteonthevecoperatorappliedtounbalancedblockstructuredmatrices AT halcaswell noteonthevecoperatorappliedtounbalancedblockstructuredmatrices AT silkefvandaalen noteonthevecoperatorappliedtounbalancedblockstructuredmatrices |
| _version_ |
1726008776446705664 |