# orthogonal vectors

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Related to orthogonal vectors: Orthonormal vectors, parallel vectors

## orthogonal vectors

[ȯr′thäg·ən·əl ′vek·tərz]
(mathematics)
In an inner product space, two vectors are orthogonal if their inner product vanishes.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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All these estimates are approximated values only, but have higher complexity due to requirement of pilot symbol or orthogonal vector generation, etc.
This relationship is helpful when two orthogonal vectors are known but not at a source angle of interest.
A general pattern of coding that can be used routinely to obtain orthogonal vectors for balanced experiments (i.e., experiments with the same number of replicates in each group) is succinctly outlined by the following matrices:
where the t's are individual regression coefficients corresponding to particular orthogonal vectors (X's), as shown in the one-way example above.
The first two columns, [X.sub.A1] and [X.sub.A2], are orthogonal vectors that code for factor A (three levels) and the third column, [X.sub.B1], codes for factor B (two levels).
Hence, relaxing the assumption that mutually exclusive states of affairs must be represented by orthogonal vectors entails that there are states which we cannot interpret.
The relaxation of the quantum mechanical dogma that mutually exclusive states of affairs must be represented by orthogonal vectors seems at first glance to be merely inelegant.
3 is A = {[a.sub.1], ..., [a.sub.9]}, and the normalized orthogonal vectors set of which is W = {[w.sub.1], ...
In our index construction scheme, we first need to build the normalized orthogonal vectors of graph vertices by Gram-Schmidt algorithm.
The results of normalized orthogonal vectors construction can be seen in Fig.
The ENOR algorithm produces a set of orthogonal vectors spanning the subspace with a reduced number of state variables.
Specifically, from the relationship of the orthogonal vectors [[??].sub.[tau]], and [[??].sub.S] in (9), it must be true that

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