Vectors & Tensors

Tensors are basically a generalization of vectors. While vectors (with direction and magnitude) are naturally suited for modeling real-life things like velocity and force, tensors had no application for the first 50+ years of their existence. It was in the mid-1800's that Hermann Grassmann and William Rowan Hamilton formulated the idea of tensors; however, partly because commutativity of multiplication doesn't apply for tensors, tensors were not widely accepted until they were later used by Albert Einstein in relativity. ¹⁰

• Rank 0 tensor: scalar
• Rank 1 tensor: vector
• Rank 2,3,4, etc.: higher-dimensional things like vectors