- #1
Frabjous
Gold Member
- 1,607
- 1,931
Is there a book that emphasizes performing calculations with tensors in modern notation?
caz said:How Socratic. I actually do not know. I have an index intensive understanding and am looking for something more. I am guessing it is a modern formulation of differential geometry, but I do not know for sure. I am an applied sort of person, so I am more interested in learning how to do calculations than in proofs.
Tensors are mathematical objects that describe the relationships between different physical quantities. They are important in modern notation because they allow for more efficient and elegant calculations in fields such as physics, engineering, and computer science.
In modern notation, tensors are represented using index notation, where each index represents a specific direction or component. This allows for easier manipulation and calculation of tensor quantities.
Some common operations that can be performed with tensors in modern notation include addition, multiplication, contraction, and transformation. These operations allow for the manipulation and transformation of tensor quantities to solve various problems.
Yes, tensors can be used in any number of dimensions. In fact, tensors are often used to describe physical quantities in higher dimensions, such as in the study of relativity and quantum mechanics.
Tensors are used in machine learning and data analysis to represent and manipulate large datasets. They allow for efficient processing and analysis of complex data, making them essential in these fields.