Undergrad Difference between tensor and vector?

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The Kronecker delta, δij, is classified as a rank 2 tensor because it can be represented as a matrix, while a vector is a rank 1 tensor. The discussion confirms that a scalar is a rank 0 tensor, and the hierarchy of tensor ranks is clarified. Participants agree on the definitions and relationships between tensors, vectors, and scalars. The conversation also includes a reference to additional resources for further understanding. Overall, the distinction between tensors and vectors is emphasized through their respective ranks.
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δij is the Kronecker delta - is this considered a tensor or vector? I know it means the identity when i=j so I'm going to guess tensor because it's a matrix rather than just a vector but I want to make sure. A matrix is a rank 2 tensor and a vector is a rank 1 and a scalar is a rank 0? How does that work?
 
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Okay awesome! Thank you for the clarification and link
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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