Difference between revisions of "Partitioned Matrix"
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A partioned matrix may group specific sectors within an economy or represent a sector-country decomposition in a [[Multiregional Input-Output Model]]. An MRIO model extends the standard IO matrix to a larger system where each industry in each country has a separate row and column.<ref>R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009</ref> | A partioned matrix may group specific sectors within an economy or represent a sector-country decomposition in a [[Multiregional Input-Output Model]]. An MRIO model extends the standard IO matrix to a larger system where each industry in each country has a separate row and column.<ref>R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009</ref> | ||
| − | If a matrix is partitioned into four blocks, it can be inverted blockwise (Schur Complement) | + | If a matrix is partitioned into four blocks, it can be inverted blockwise (Using the concet pf [[wikipedia:Schur complement | Schur Complement]]). |
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== See Also == | == See Also == | ||
Revision as of 18:07, 18 September 2023
Definition
A Partitioned Matrix (or Block Matrix) is the general mathematical structure used prominently in the context of Multiregional Input-Output Model. It divides n industries in the Input-Output Model into subgroups.
Usage
A partioned matrix may group specific sectors within an economy or represent a sector-country decomposition in a Multiregional Input-Output Model. An MRIO model extends the standard IO matrix to a larger system where each industry in each country has a separate row and column.[1]
If a matrix is partitioned into four blocks, it can be inverted blockwise (Using the concet pf Schur Complement).
See Also
Further Resources
References
- ↑ R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009
