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mohammed El-Kady
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Can anyone illustrate for me matrix decomposition in a simple way?
mohammed El-Kady said:Can anyone illustrate for me matrix decomposition in a simple way?
It's the decomposition into a orthogonal rotation ##U## and a symmetric positive definite stretching ##P##, see the polar decomposition https://en.wikipedia.org/wiki/Polar_decompositionmohammed El-Kady said:thank you for your responses, while i study elasticity it have been mentioned that deformation tensor is stretch and rotation tensor and the proof by using matrix decomposition, I've no idea about the type of decomp.
thank you too much, its helpful and valuable and easyfresh_42 said:It's the decomposition into a orthogonal rotation ##U## and a symmetric positive definite stretching ##P##, see the polar decomposition https://en.wikipedia.org/wiki/Polar_decomposition
Matrix decomposition, also known as matrix factorization, is a mathematical process that breaks down a complex matrix into smaller, simpler matrices. This allows for easier manipulation and analysis of the data within the matrix.
There are several types of matrix decomposition, including LU decomposition, QR decomposition, and singular value decomposition (SVD). Each type has its own unique approach and application.
Matrix decomposition is commonly used in data analysis to reduce the dimensionality of a dataset, identify patterns and relationships between variables, and make predictions based on the decomposed matrix.
Imagine you have a matrix that represents the grades of students in a class. By decomposing the matrix, you can identify which students are performing well in which subjects, and group them accordingly. This can help with identifying areas of improvement and overall performance of the class.
The main advantage of matrix decomposition is that it simplifies complex data and allows for easier analysis and interpretation. It also helps to reduce the number of variables and can improve the accuracy of predictions and models. Additionally, different types of matrix decomposition have different advantages, making it a versatile tool for various applications.