Abstract
Real distinct principal powers and corresponding perpendicular meridians of a lens or surface combine as factors of a 2×2 power matrix for calculation. A scalar matrix that represents the nearest sphere power component, may be extracted from this. Non-spherical or astigmatic matrix power component(s) remain. The purpose of this paper is to analyse the contribution that astigmatic components in two planes make to the lens power. These basic power members of the set of matrix basic components provide the preferred meridians as they combine linearly to complete the power matrix of a lens or surface. Essentially invertible independent matrices make for symmetric basic components. The maximum number of mutually orthogonal matrices in a vector space of finite dimension form a basis for that space. Properties of basic matrices are latent in the use of optometric power vectors. This paper attempts to make the case for the explicit mention of orthogonal bases of matrices in order to support calculations of power.
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