Higher Order Tensor: Learn Calculation Rules & Get Info

In summary, a higher order tensor is a multi-dimensional mathematical object that extends the concept of vectors and matrices. It has various real-world applications in fields such as physics, engineering, and computer science. The calculation rules for higher order tensors are similar to those for matrices, involving element-wise addition and subtraction, and a combination of scalar multiplication and dot product for multiplication. To obtain information from a higher order tensor, indexing and slicing operations can be used, as well as operations like norm, trace, and determinant. There are also tools and libraries available, such as NumPy, TensorFlow, and PyTorch, that provide efficient methods for working with higher order tensors.
  • #1
blue angel
1
0
hi...
can anyone could help me by explaining about higher order tensor and it's calculation rules ? or perhaps u could give me a link to a website where i could find complete information about it. thanks...:rolleyes:
 
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  • #2
Why are you rolling your eyes?
 
  • #3
higher order than what?
 

FAQ: Higher Order Tensor: Learn Calculation Rules & Get Info

1. What is a higher order tensor?

A higher order tensor is a mathematical object that generalizes the concept of a vector and a matrix to higher dimensions. It can be thought of as a multi-dimensional array of numbers that can be manipulated using specific rules and operations.

2. What are some real-world applications of higher order tensors?

Higher order tensors have various applications in fields such as physics, engineering, and computer science. They are used in computer vision for image and signal processing, in machine learning for data analysis and pattern recognition, and in quantum mechanics for modeling physical systems.

3. What are the calculation rules for higher order tensors?

The calculation rules for higher order tensors are similar to those for matrices. Addition and subtraction of tensors are performed element-wise, while multiplication involves a combination of scalar multiplication and the dot product. Tensor multiplication follows the Einstein summation convention, where repeated indices are summed over.

4. How do I obtain information from a higher order tensor?

To obtain information from a higher order tensor, you can use indexing and slicing operations to select specific elements or sub-tensors. You can also perform operations such as the norm, trace, and determinant to get information about the magnitude, sum, and volume of the tensor, respectively.

5. Are there any tools or libraries available for working with higher order tensors?

Yes, there are several tools and libraries available for working with higher order tensors, such as NumPy, TensorFlow, and PyTorch. These libraries provide efficient methods for creating, manipulating, and performing operations on tensors, making it easier for scientists to work with them in their research.

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