## Monday, 21 November 2011

### How to find the matrix A if we known of Leontief matrix

How to find the matrix A if we known of Leontif matrix. This post is a continuation of my previous post about the Leontief inverse matrix, as well as to answer questions friend about the inverse matrix, which asks you about how to calculate the matrix technology if we known the Leontief inverse matrix.

If we let the technology matrix is a matrix A, and L is the Leontief inverse matrix.

L = (I - A) -1

then if L will be inverse again , Then will generate a matrix (I - A), illustrated by below equation
L-1 = (I - A) -1 = ((I - A) -1) -1 = (I - A)
then the matrix A can be calculated:
I - A = (I - A)
-A = (I - A)-I
A = absolute((I - A)-I)

Based on equation of the matrix above, then by using excel the above equation can be calculated with the following guidelines:

1. Create a table as below

2. Compute the inverse Leontief inverse matrix
((I - A) -1) -1
Block range A7: C9, type formula:
= MINVERSE (A2: C4)
press combination button Ctrl + Shift + Enter
Compute the matrix A = (I-A)-I
Block range E7: G9
= ABS (A7: C9-E2: G4)
press Ctrl + Shift + Enter

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3. The blog was absolutely fantastic! Lots of great information and
inspiration, both of which we all need!b Keep 'em coming... you all do
such a great job at such Concepts... can't tell you how much I, for
one appreciate all you do!