Tensor Analysis in vector and matrix algebra notation

Thread starter NotASmurf
Start date Jan 15, 2015
Tags

Algebra Analysis Matrix Matrix algebra Notation Tensor Tensor analysis Vector

In summary, tensor analysis is a branch of mathematics that deals with multi-dimensional arrays of numbers called tensors, which represent relationships between vectors and matrices. It uses vector and matrix algebra to manipulate and analyze tensors. Tensor analysis is important in various fields such as physics, engineering, and computer science due to its ability to solve complex problems efficiently. It has a wide range of applications including mechanics, electromagnetism, quantum mechanics, relativity, computer vision, and machine learning. Common operations in tensor analysis include multiplication, contraction, and transformation, which allow for the manipulation and extraction of meaningful information from data.

Jan 15, 2015

NotASmurf

Is there anywhere that teaches tensor analysis in both tensor and non tensor notation, because I'm having to pause each time i look at something in tensor notation and phrase it mentally in non tensor notation at which point it becomes staggeringly simpler. Any help apreciated

Physics news on Phys.org

Jan 15, 2015

mathman

Science Advisor

I believe the Math Forum would be a better place for you question.

Related to Tensor Analysis in vector and matrix algebra notation

What is tensor analysis?

Tensor analysis is a branch of mathematics that deals with the study of tensors, which are multi-dimensional arrays of numbers that describe the relationships between vectors and matrices. It involves using vector and matrix algebra notation to manipulate and analyze tensors.

What are tensors?

Tensors are multi-dimensional arrays of numbers that represent geometric quantities in a coordinate-independent manner. They are used to describe the relationships between vectors and matrices, and can have any number of dimensions.

Why is tensor analysis important?

Tensor analysis is important because it provides a powerful tool for understanding and solving problems in fields such as physics, engineering, and computer science. It allows for the manipulation and analysis of complex relationships between vectors and matrices in a concise and efficient manner.

What are some applications of tensor analysis?

Tensor analysis has a wide range of applications in various fields, including mechanics, electromagnetism, quantum mechanics, relativity, and computer vision. It is also used in machine learning and deep learning algorithms for data analysis and pattern recognition.

What are some common operations in tensor analysis?

Some common operations in tensor analysis include tensor multiplication, contraction, and transformation. These operations allow for the manipulation and transformation of tensors to solve complex problems and extract meaningful information from data.