Decomposition and scaling-inequality for line-sum-symmetric nonnegative matrices
Technical Report
·
OSTI ID:5436047
A matrix B is called line-sum-symmetric if it is square and the sum of elements in each row of B equals the sum of elements in the corresponding column. Results from the theory of network flows are used to obtain a decomposition of nonnegative line-sum-symmetric matrices. The decomposition is employed to prove the following inequality: Assume D(x)AD(y) is line-sum-symmetric where A is a square, nonnegative matrix and D(x) and D(y) are diagonal matrices whose diagonal elements are the coordinates of the nonnegative vectors x and y, respectively. Then y/sup T/Ax greater than or equal to x/sup T/Ay.
- Research Organization:
- Stanford Univ., CA (USA). Systems Optimization Lab.
- DOE Contract Number:
- AT03-76ER72018
- OSTI ID:
- 5436047
- Report Number(s):
- SOL-83-21; ON: DE84005639
- Resource Relation:
- Other Information: Portions are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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