Orthogonal

Pronunciation: /ɔrˈθɒ.gə.nl/ Explain
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Manipulative 1 - Orthogonal Lines Created with GeoGebra.

Two lines are orthogonal if they are perpendicular at the point of intersection. Two curves are orthogonal at a point of intersection if they are perpendicular at the point of intersection.

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Manipulative 2 - Orthogonal Curves Created with GeoGebra.
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Manipulative 3 - Orthogonal Vectors Created with GeoGebra.

Two vectors are orthogonal if the inner product of the vectors is zero. When graphing orthogonal vectors, the vectors are perpendicular to each other.

Two square matricies of the same dimensions are orthogonal if the product of the matrices is the identity matrix. See figure 1.

[\\array{1 & 3 & -2 \\\\ 0 & -2 & 1 \\\\1 & 0 & 5}\\right]\\;\\cdot\\;\\left[\\array{\\frac{10}{11} & \\frac{15}{11} & \\frac{1}{22} \\\\ -\\frac{1}{11} & -\\frac{7}{11} & \\frac{1}{22} \\\\ -\\frac{2}{11} & -\\frac{3}{11} & \\frac{1}{11}}\\right]\\;=\\;\\left[\\array{1 & 0 & 0 \\\\ 0 & 1 & 0 \\\\ 0 & 0 & 1}\\right]
Figure 1: Orthogonal matrices

References

  1. McAdams, David E.. All Math Words Dictionary, orthogonal. 2nd Classroom edition 20150108-4799968. pg 132. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

 McAdams, David E. Orthogonal. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/o/orthogonal.html.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/5/2018: Removed broken links, updated license, implemented new Geogebra protocol, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/21/2009: Added "References". (McAdams, David E.)
10/9/2008: Initial version. (McAdams, David E.)

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