title: Algebra of sphero-cylinders and refractive errors, and their means, variance, and standard deviation.
abstract: 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.
authors.affiliation: Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa.
authors.forename: W F
authors.initials: WF
authors.lastname: Harris
mesh_terms: D006801:Humans; D008433:Mathematics; D012030:Refractive Errors / Q000503:physiopathology*; D013223:Statistics as Topic