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chandran
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why the concept of tensor was invented. I always see that tensors are provided in matrix format. example inertia tensor is there in a 3x3 matrix.
why?
why?
There are quantities used in physics for which the concept of a number or a vector is insufficient. A more general notion of a geometrical object was required. The number (scalar) and vector were defined as tensors of a lower "rank" and then tensors of higher rank were defined. Two such tensos come to mind. The tidal force tenso which are found herechandran said:why the concept of tensor was invented. I always see that tensors are provided in matrix format. example inertia tensor is there in a 3x3 matrix.
why?
A tensor is a mathematical object that describes the relationship between vectors and matrices in a multidimensional space. It is different from a vector in that it has both magnitude and direction, and different from a matrix in that it can have more than two dimensions.
The concept of tensor was invented to help describe and analyze complex physical phenomena, such as fluid dynamics and electromagnetism, which cannot be fully understood using traditional vector and matrix mathematics. Tensors allow for a more precise and comprehensive representation of these phenomena.
Yes, tensors have applications in various fields such as engineering, computer science, and data analysis. They are used to model and analyze complex systems and relationships in these fields.
Tensors can be challenging to grasp at first, as they involve complex mathematical concepts and notation. However, with practice and a solid understanding of linear algebra, they can be effectively used and manipulated in various applications.
The concept of tensor has greatly enhanced our understanding of the physical world by providing a more accurate and comprehensive mathematical framework for describing and analyzing complex phenomena. It has allowed for the development of advanced theories and models in physics, leading to significant advancements in various fields such as astrophysics, quantum mechanics, and relativity.