The eigenvectors have very important properties called orthogonality properties. The concept of normality generalizes to orthogonality. The concept of normality generalizes to orthogonality (right angles). Synchronous CDMA exploits mathematical properties of orthogonality between vectors representing the data strings. The case of a pseudo-Euclidean plane uses the term hyperbolic orthogonality. These theorems can be proven using the orthogonality property. The operation of a lock-in amplifier relies on the orthogonality of sinusoidal functions. In the absence of reflexivity we have to distinguish left and right orthogonality. This ensures the orthogonality of all the generated vectors. They also provide the means of defining orthogonality between vectors (zero inner product). This method includes a technique that minimizes grid smoothness, orthogonality and volume variation. It is difficult to check numerically the linear dependence or exact orthogonality. In order to achieve orthogonality, additional constraints must be enforced. We would like to minimize the angle distortion to preserve orthogonality. Listing's law can be deduced without starting with the orthogonality assumption.