Social Research Glossary   A B   Citation reference: Harvey, L., 2012-20, Social Research Glossary, Quality Research International, http://www.qualityresearchinternational.com/socialresearch/ This is a dynamic glossary and the author would welcome any e-mail suggestions for additions or amendments. Page updated 19 December, 2019 , © Lee Harvey 2012–2020. A fast-paced novel of conjecture and surprises

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Orthogonality

core definition

Two factors are orthogonal when they are uncorrelated with each other or, in mathematics, when two lines are perpendicular.

explanatory context

analytical review

Rogers et al. (1984) state:

Linearly independent, orthogonal, and uncorrelated are three terms used to indicate lack of relationship between variables.

Wolfram MathWorld (1999–2019) states:

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection.

Hosch (2009) states:

Orthogonality, In mathematics, a property synonymous with perpendicularity when applied to vectors but applicable more generally to functions. Two elements of an inner product space are orthogonal when their inner product—for vectors, the dot product (see vector operations); for functions, the definite integral of their product—is zero. A set of orthogonal vectors or functions can serve as the basis of an inner product space, meaning that any element of the space can be formed from a linear combination (see linear transformation) of the elements of such a set.

associated issues

Hosch, 2009, 'Orthogonality', Encyclopaedia Britannica, available at https://www.britannica.com/science/orthogonality, accessed 12 June 2019.

Rogers, J.L., Nicewander, W.A. and Toothaker, L., 1984, 'Linearly independent, orthogonal, and uncorrelated variables', American Statistician, 38(2), available at http://terpconnect.umd.edu/~bmomen/BIOM621/LineardepCorrOrthogonal.pdf, accessed 24 December 2016.'not found' 12 June 2019.

Wolfram MathWorld , 1999–2019, 'Orthogonal', available at http://mathworld.wolfram.com/Orthogonal.html, accesed 12 June 2019.

related areas

factor analysis

multivariate analysis

Sources