# reciprocal matrix

## reciprocal matrix

[ri¦sip·rə·kəl ′mā·triks]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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In AHP, the paired difference is measured by the ratio scale and correspondingly P is a pairwise reciprocal matrix (PRM).
8), which is the average CI of a randomly generated reciprocal matrix. CI=0 indicates perfectly consistent matrix, otherwise, CI should be positive.
Attention: A should satisfy the following properties: [a.sub.ij] > 0, = [a.sub.ij], and [a.sub.ii] = 1; A is called positive reciprocal matrix.
The consistent completion of a reciprocal matrix as a mechanism to obtain a consistent body of opinion issued in an incomplete manner by a specific actor was addressed.
The matrix is called the fuzzy positive reciprocal matrix, MM = [[[m.sub.ij]].sub.n*n].
Saaty [21] demonstrated that for consistent reciprocal matrix, the largest eigenvalue is equal to the number of comparisons, or [[lambda].sub.max] = n.
matrix A represents a reciprocal matrix, [a.sub.ij] is the inverse of the entry [a.sub.kj] which indicates the relative importance of [C.sub.i] compared with attribute [C.sub.j].
Where matrix A represents a reciprocal matrix, [a.sub.ij] is the inverse of the entry [a.sub.kj] which indicates the relative importance of [C.sub.i] compared with attribute [C.sub.j].
It is known that the maximum eigenvalue of the reciprocal matrix of range m is [[lambda].sub.max]=m (Saaty 1980).
(3) Measurement consistency It is necessary to measure the level of consistency of the reciprocal matrix by a consistency index (CI).
So, the reciprocal matrix A of average acoustic velocity in each block can be calculated as
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