🎬Visualize the geometric transformation of the Kronecker delta on a cube

The Kronecker delta is a mathematical tool for transforming space. It's not just a symbol that equals 1 or 0; it represents a specific type of geometric operation. When the indices are the same, it acts as an identity transformation. The space (represented by the cube) remains unchanged, and its volume is preserved. This corresponds to the Kronecker delta's value of 1. When the indices are different, it acts as a collapsing transformation. The space is flattened, and its volume is reduced to zero. This corresponds to the Kronecker delta's value of 0. The higher-order tensor extension shows this principle applies to more complex scenarios, where a transformation can collapse a 3D space in multiple dimensions, but the core idea of preserving or collapsing space remains the same.

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