Difference between revisions of "Partitioned Matrix"
Wiki admin (talk | contribs) |
Wiki admin (talk | contribs) |
||
| Line 8: | Line 8: | ||
== Tensor Representation == | == Tensor Representation == | ||
| − | An N th | + | An N-th order tensor is an element of the tensor product of N vector spaces, each of which has its own coordinate system. Slices are two-dimensional sections of a tensor, defined by fixing all but two indices. |
| − | Matricization | + | Matricization (also known as unfolding or Mode-k flattening) is the process of reordering the elements of an N-th order array into a matrix. |
== See Also == | == See Also == | ||
Revision as of 17:29, 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 (Schur Complement)
Tensor Representation
An N-th order tensor is an element of the tensor product of N vector spaces, each of which has its own coordinate system. Slices are two-dimensional sections of a tensor, defined by fixing all but two indices.
Matricization (also known as unfolding or Mode-k flattening) is the process of reordering the elements of an N-th order array into a matrix.
See Also
Further Resources
References
- ↑ R.E. Miller and P.D. Blair, Input-Output Analysis: Foundations and Extensions, Second Edition, Cambridge University Press, 2009
