Difference between revisions of "Aggregation Matrix"
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Aggregation can be for example along sectoral or regional dimensions. | Aggregation can be for example along sectoral or regional dimensions. | ||
− | Vectors and Matrices can be aggregated by multiplying with the aggregation matrix. Mathematically a aggregation matrix T is a <math>K \times N</math> matrix, where each value <math> | + | Vectors and Matrices can be aggregated by multiplying with the aggregation matrix. Mathematically a aggregation matrix T is a <math>K \times N</math> matrix, where each value <math>s_{mn}</math> is either zero or one. |
:<math>S=\left(\begin{matrix} | :<math>S=\left(\begin{matrix} | ||
− | + | s_{00} & s_{01} & \dots &s_{0n} & \dots & s_{0N} \\ | |
− | + | s_{10} & s_{11} & \dots &s_{1n} & \dots & s_{1N} \\ | |
\vdots & \vdots & \ddots &\vdots & \ddots & \vdots \\ | \vdots & \vdots & \ddots &\vdots & \ddots & \vdots \\ | ||
− | + | s_{m0} & s_{m1} & \dots &s_{mn} & \dots & s_{mN} \\ | |
\vdots & \vdots & \ddots & \vdots& \ddots & \vdots \\ | \vdots & \vdots & \ddots & \vdots& \ddots & \vdots \\ | ||
− | + | s_{K0} & s_{K1} & \dots & s_{Kn} & \dots & s_{KN}\\ | |
− | \end{matrix}\right).</math> | + | \end{matrix}\right). |
+ | </math> | ||
=== Vector Quantity Aggregation === | === Vector Quantity Aggregation === |
Revision as of 17:38, 20 November 2023
Contents
Definition
Aggregation Matrix in the context of Input-Output Analysis is a Boolean Matrix that aims to produce a coarse-grained version of a more granular Input-Output Model.
Aggregation can be for example along sectoral or regional dimensions.
Vectors and Matrices can be aggregated by multiplying with the aggregation matrix. Mathematically a aggregation matrix T is a matrix, where each value is either zero or one.
Vector Quantity Aggregation
A vector of dimension N is aggregated through its pre-multiplication with the aggregation matrix.
Matrix Quantity Aggregation
A matrix of dimension N is aggregated through its pre-multiplication with the aggregation matrix and the post-multiplication with the aggregation matrix transpose.