Tensor operations and properties

In summary, the speaker recently finished school and is now preparing for their studies in physics. They are interested in learning more about the mathematics used in physics, particularly tensors. They are asking for recommendations for resources to help them understand tensors better. Two ebook and a book suggestion were provided by other users.
  • #1
Marin
193
0
Hello everyone!

I finished school 2 months ago and at the moment I'm looking forward to my study in physics :)

As a preparation for it, I want to learn more about the mathematics physics use :)

I read some books about vectors and matrices and came upon the term 'tensor' several times :)

I was wondering, if anyone of you knows a site or a script on the internet where all the properties of tensors, or at least the general ones are well explained, so that an amateur like me could try to understand them :)


Thanks in advance!

with best regards, Marin
 
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  • #3
Thanks, ForMyThunder!

I'll take a look at them when I have time :)
 
  • #4
No problem. =]
 

1. What are tensors and why are they important in science?

Tensors are mathematical objects that represent physical quantities with both magnitude and direction. They are used in many fields of science, including physics, engineering, and computer science, to describe and model complex systems and processes.

2. What are the basic operations that can be performed on tensors?

The basic tensor operations include addition, subtraction, multiplication, and division. These operations are performed on individual elements of tensors or on entire tensors to manipulate and transform their values.

3. What are some important properties of tensors?

Some key properties of tensors include their rank, which is the number of indices needed to describe the tensor, and their dimensionality, which is the number of components or elements in the tensor. Other properties include symmetry, skew-symmetry, and orthogonality, which describe the relationships between different components of a tensor.

4. How are tensors used in machine learning and artificial intelligence?

In machine learning and artificial intelligence, tensors are used to represent and process complex data such as images, text, and speech. They are also used in deep learning algorithms to train neural networks and make predictions based on large amounts of data.

5. What are some real-world applications of tensor operations?

Tensor operations have numerous applications in science and technology, including image and signal processing, fluid dynamics, material science, and quantum mechanics. They are also used in everyday technologies such as GPS systems, medical imaging, and computer graphics.

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