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===Methods===
====Separable
Given the equation AX=ZB, it is possible to decompose the equation into a purely rotational and translational part; methods utilizing this are referred to as separable methods. Where '''R'''<sub>A</sub> represents a 3x3 rotation matrix and '''t'''<sub>A</sub> a 3x1 translation vector, the equation can be broken into two parts:<ref>[https://arxiv.org/pdf/1907.12425.pdf]</ref>
:'''R'''<sub>A</sub>'''R'''<sub>X</sub>='''R'''<sub>Z</sub>'''R'''<sub>B</sub>
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Equation 2 becomes linear if '''R'''<sub>Z</sub> is known. As such, the most frequent approach is to Rx and Rz using the first equation then using it to solve for the second two variables in the second equation. Rotation is represented using [[quaternion]]s, allowing for a linear solution to be found. While separable methods are useful, any error in the estimation for the rotation matrices is compounded when being applied to the translation vector.<ref>[https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=910651], page 3. </ref> A solution to this is a simultaneous method, which calculates both at the same time.
====Simultaneous
By formulating the matrices as [[dual quaternion]]s, it is possible to get a linear equation by which X is solvable in a linear format.<ref>[https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=910651]</ref>
====Iterative solutions====
*[http://math.loyola.edu/~mili/Calibration/]
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{{collapse top| What is Algebra}}
==What is algebra?==
Algebra is a complex branch of mathematics in which many subjects are vastly different from others. Essentially, algebra is manipulation of symbols and operations based on given properties about them.<ref>I. N. Herstein, ''Topics in Algebra'', "An algebraic system can be described as a set of objects together with some operations for combining them." p. 1, Ginn and Company, 1964</ref> For instance, elementary algebra is about manipulating variables, which are abstractions of numbers in a number system. The variables in the number system are only allowed to have properties that are shared by every number it represents, and vice versa.
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