Relativity #29.1 - Metrics, Inner Products and Norms скачать в хорошем качестве

Relativity #29.1 - Metrics, Inner Products and Norms

Notes are on my GitHub! github.com/rorg314/WHYBmaths This video is the start of a brief interlude to clarify some common terminology surrounding metrics. I discuss how we can define an "inner product" between vectors using a metric tensor, and how this can be understood using the raising and lowering property of the metric. I then introduce the concept of a "norm", a scalar quantity that can be constructed using the metric, that we conventionally take to represent a geometric "distance". In the upcoming videos, we will discuss the Minkowski metric and norm, and how this is an invariant quantity under a particular set of transformations (the Lorentz transformations).