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Bookmark or Share- What are the Differences Between a Matrix and a Tensor?The components of a rank-2 tensor can be written in a matrix. The tensor is not that matrix, because different types of tensors can correspond to the same matrix. The differences between those tensor types are uncovered by the basis transformations (hence the physicist's definition: "A tensor is what transforms like a tensor").
- An Introduction to Tensors - Mathematics Stack ExchangeA tensor field of type $(0, 0)$ is a smooth function. A tensor field of type $(1, 0)$ is a vector field. A tensor field of type $(0, 1)$ is a differential $1$-form. A tensor field of type $(1, 1)$ is a morphism of vector fields. A tensor field of type $(0, 2)$ which is symmetric and nondegenerate is a metric tensor.
- What Is a Tensor? The mathematical point of view. - Physics ForumsThe tensor product of two 1 dimensional vector spaces is 1 dimensional so it is smaller not bigger than the direct sum. The tensor product tof two 2 dimensional vector spaces is 4 dimensional so this is the the same size as the direct sum not bigger.This is correct but missing the relevant point: that the presentation contains a false statement.
- manifolds - Difference Between Tensor and Tensor field? - Mathematics ...A tensor field has to do with the notion of a tensor varying from point to point . A scalar is a tensor of order or rank zero , and a scalar field is a tensor field of order zero . A vector is a tensor of order or rank one , and a vector field is a tensor field of order one . Some additional mathematical details.
- Exploring Rank 3 Tensors for Beginners - Physics ForumsThe gradient of a rank 2 tensor (matrix) in a coordinate system (vector), is a rank 3 tensor. (GAMUDD) in example below. Another example is the gradient of the metric in general relativity which is the connection.
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