A rank-1 tensor is a mathematical object that can be represented as a one-dimensional array of components, essentially behaving like a vector. It plays a crucial role in various fields such as physics and engineering, especially when discussing quantities that have both magnitude and direction, like forces or velocities. Rank-1 tensors are foundational in expressing concepts like divergence, curl, and gradient, and they interact seamlessly with both covariant and contravariant vectors in tensor notation.
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