Thank you so much! You're a life saver. This got me so confused. QR decomposition just clicked for me about 5 minutes ago, and now I get this too!andrewkirk said:
Cholesky Decomposition is a method used in linear algebra to decompose a symmetric, positive definite matrix into the product of a lower triangular matrix and its transpose.
Cholesky Decomposition is important because it can be used to solve systems of linear equations efficiently and accurately, especially for large matrices. It is also used in other mathematical applications such as optimization and data analysis.
Cholesky Decomposition is unique in that it only works for symmetric, positive definite matrices, while other decompositions like LU decomposition and QR decomposition can work for a wider range of matrices. Additionally, Cholesky Decomposition produces a lower triangular matrix as one of its factors, while other decompositions may produce a combination of upper and lower triangular matrices.
Cholesky Decomposition is commonly used in numerical linear algebra for solving systems of linear equations, computing matrix inverses, and performing least squares regression. It is also used in machine learning algorithms, such as principal component analysis and linear discriminant analysis.
No, Cholesky Decomposition is only possible for symmetric, positive definite matrices. If a matrix does not meet these criteria, then Cholesky Decomposition cannot be performed. In these cases, other matrix decompositions may be used instead.