Difference between revisions of "Partitioned Matrix"
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| + | == 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.<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 (Using the concet of the [[wikipedia:Schur complement | Schur Complement]]). | ||
| + | |||
| + | == See Also == | ||
| + | * [[Aggregation Matrix]] | ||
| + | |||
| + | == Further Resources == | ||
| + | * [https://www.openriskacademy.com/course/view.php?id=70 Crash Course on Input-Output Model Mathematics] | ||
| + | * [https://www.openriskacademy.com/course/view.php?id=64 Introduction to Input-Output Models using Python] | ||
| + | |||
| + | == References == | ||
| + | * [[wikipedia:Block matrix | Block Matrix @ Wikipedia]] | ||
| + | <references/> | ||
| + | |||
| + | [[Category:EEIO]] | ||
| + | |||
| + | {{#set:Has Formula = HAS_FORMULA}} | ||
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Latest revision as of 18:33, 16 November 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 of the 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
