5.3 Determinants in practice
In the theory and practice of mathematics, the development of concepts usually has a simple flow. Definitions first arise from vague geometric or algebraic intuitions, eventually crystallizing in mathematical formalism.
However, mathematical definitions often disregard practicalities. For a very good reason, mind you! Keeping practical considerations out of sight gives us the power to reason about structure effectively. This is the strength of abstraction. Eventually, if meaningful applications are found, the development flows toward computational questions, putting speed and efficiency onto the horizon.
The epitome of this is neural networks themselves. From theoretical constructs to state-of-the-art algorithms that run on your smartphone, machine learning research followed this same arc.
This is also what we experience in this book on a microscopic level. Among many other examples, think about determinants. We introduced the determinant as the orientation...
