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Am J Optom Physiol Opt. 1988 Oct;65(10):794-802.

Algebra of sphero-cylinders and refractive errors, and their means, variance, and standard deviation.

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Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa.


Sphero-cylinders and refractive errors can be represented by matrices. Matrix algebra provides methods whereby sphero-cylinders can be added, subtracted, multiplied, inverted, and raised to powers and can have roots extracted. These operations are defined for sphero-cylinders and examples are given. In terms of these operations a number of means of refractive errors are defined: the arithmetic, harmonic, and quadratic means. Furthermore it is possible to define a variance and standard deviation for refractive errors. These quantities should provide a basis for a formal approach to the statistical analysis of populations of refractive errors.

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