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What does orthogonal mean?

Looking for the meaning or definition of the word orthogonal? Here's what it means.

Adjective
  1. (geometry) Of two objects, at right angles; perpendicular to each other.
  2. (mathematics)
    1. Of a pair of vectors: having a zero inner product; perpendicular.
    2. Of a square matrix: such that its transpose is equal to its inverse.
    3. Of a linear transformation: preserving its angles.
    4. Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.
  3. (statistics) Statistically independent, with reference to variates.
  4. (software engineering) Of two or more aspects of a problem, able to be treated separately.
  5. Of two or more problems or subjects, independent of or irrelevant to each other.
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Examples
The original edition contained an early example of a problem about orthogonal Latin squares.
This factor analysis was based on the combined normative samples using principal factoring with iteration plus orthogonal rotation.
To the left, an orthogonal void cut like a proscenium or picture frame is clearly a signal of something important deep in the interior.
We scored shield color by reference to the Munsell color scale that breaks color into three orthogonal measures of hue, value, and intensity.
In resolving the differences between the orthogonal basic plan and the circular forms of the domes, perimeter walls become serrated in plan.
Other isolated instances of orthogonal polynomials occurring in the work of various mathematicians is mentioned later.

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