Tensor tensor in one article

What is a tensor

There are many ways to define tensor. Here we only discuss the concepts in the field of artificial intelligence.

In the field of artificial intelligence, the definition is relatively simple. TensorFlow is defined as follows:

A tensor is a generalization of vectors and matrices to potentially higher dimensions.

A simple translation is:Tensors are multidimensional arrays, the purpose of which is to push vectors and matrices to higher dimensions.

 

Relationship of scalar, vector, matrix, tensor

These 4 concepts are constantly rising in dimensionality. It is easier to understand the metaphorical explanation with the concept of point-line polyhedron:

Relationship of scalar, vector, matrix, tensor

Interested parties can learn more about the following:

'Understanding scalars in one article"

'Understanding Vectors in One Article"

'Understanding matrices in one article"

'Understand tensor in one article"

 

Baidu Encyclopedia and Wikipedia

Baidu Encyclopedia version

The tensor theory is a sub-discipline of mathematics and has important applications in mechanics. The term tensor originated from mechanics. It was originally used to represent the stress state at various points in an elastic medium. Later, tensor theory developed into a powerful mathematical tool for mechanics and physics. The tensor is important because it satisfies all the characteristics that the laws of physics must be independent of the choice of the coordinate system. The tensor concept is a generalization of the vector concept, and the vector is a first-order tensor. A tensor is a multilinear function that can be used to represent a linear relationship between some vectors, scalars, and other tensors.

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Wikipedia version

In mathematics, tensor is a geometric object that maps geometric vectors, scalars, and other tensors to the resulting tensor in a multilinear fashion. Therefore, the vectors and scalars that are commonly used in basic physics and engineering applications are themselves considered to be the simplest tensors. In addition, a vector from a double space providing a vector space of a geometric vector is also included as a tensor. In this case, geometry is primarily intended to emphasize the independence of any coordinate system selection.

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