We're going to dive into some introductory material to help understand the mathematics of quaternions. They are an extension of complex numbers to higher order dimensionality, and are an alternative to more conventional vector analysis that are very useful in describing both rotations in 3d computer graphics as well as the quantum mechanics of spin.
Recent neural net research incorporate the principals of quaternions into neural network architectures with quaternion convolutional neural networks. We will be diving into the QCNN architecture(s) in a future HTC post.
The following video presentation is a great gentle introduction into visualizing the mathematics of quaternions through the use of stereographic projections. Hopefully it can help you develop a more intuitive understanding of what quaternions are really all about.
So why do we care about this stuff. QCNNs utilize the properties of quaternions to help provide rotational invariance. And quaternion interpolation provides a great way to manipulate object rotation in 3 space that avoids the problems associated with other more conventional vector techniques.