Metric Tensor: Definition

This lecture covers the definition and properties of the metric tensor, which allows controlling geometric quantities and lengths. Starting with the basic definition, the instructor explains how the metric tensor influences the change of geometric entities and enables the calculation of areas between maps and surfaces. Through various examples and applications, the lecture delves into the significance of the metric tensor in determining lengths, dot products, and scalar products. The presentation concludes with a detailed exploration of symmetric matrices and their relation to the metric tensor.