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Math Nerds Unite!
Math Newb Wants to know what a Tensor is
- Context: Undergrad
- Thread starter StonedPanda
- Start date
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- Tensor
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SUMMARY
A tensor is a mathematical object that generalizes vectors and scalars, defined by its transformation properties under coordinate changes. Specifically, tensors maintain their form across different coordinate systems, making them essential in expressing physical laws. Scalars are tensors of rank 0, vectors are tensors of rank 1, and higher-rank tensors can take multiple vectors as input and produce numbers or other vectors as output. Tensors are extensively used in differential geometry and general relativity, where they describe physical phenomena in curved spaces.
PREREQUISITES- Understanding of basic vector and scalar concepts
- Familiarity with coordinate systems and transformations
- Knowledge of linear algebra, particularly matrices
- Basic principles of differential geometry
- Study the properties of tensors in differential geometry
- Learn about covariant and contravariant tensors
- Explore the application of tensors in general relativity
- Investigate tensor notation and operations, including contraction and product
This discussion is beneficial for high school students preparing for advanced mathematics, physics enthusiasts, and anyone interested in the foundational concepts of tensors and their applications in science and engineering.