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Table 13. Variables, Constants and Symbols Used in Derivation of Total Requirements Table

Monday, June 30, 2014

Excel

Variable/ Constant Notation Type Description
q Column vector Commodity output vector. Shows the total amount of the output of a commodity.
g Column vector Industry output vector. Shows the total amount of an industry’s output, including its production of scrap.
U Matrix Intermediate use table. Commodity-by-industry matrix in which each entry in a column shows the amount of each commodity used by the industry, including non-comparable imports, scrap, and second-hand goods.
V Matrix Adjusted make table. Industry-by-commodity matrix in which entries in each column show the amount of the commodity made by each industry. Adjusted to show zero entries in the column for scrap.
B Matrix Use coefficient matrix. Commodity-by-industry matrix in which each entry in a column show the amount of a commodity that an industry used per dollar of its output. Derived from matrix U.
D Matrix Market share matrix. Industry-by-commodity matrix in which each entry in a column shows the share of an industry in total output of a given commodity. Derived from matrix V.
W Matrix Transformation matrix. Industry-by-commodity matrix in which each entry in a column shows the share of an industry in total output of a given commodity, with each industry’s commodity share adjusted for scrap produced by the industry. Derived from matrix D and vector p.
i Column vector Unit vector. All entries are 1.
I Matrix Identity matrix. Square matrix in which value of 1 appears in the main diagonal cells and the value of zero appears in all other cells.
- Matrix Diagonal matrix. Symbol used to indicate a diagonal matrix. When placed over a vector, it indicates a square matrix in which the elements of the vector appear in the main diagonal cells and zeros in the other cells.
^ Symbol Symbol that when placed over a vector, indicates a square matrix.

SOURCE: U.S. Department of Transportation, Bureau of Transportation Statistics, 2014