 1:34 AM
@MartinSleziak thanks that's great.

6 hours later… 7:08 AM
A new tag was created by Rodrigo de Azevedo and added to 16 questions. The same user created a tag-excerpt. Cholesky decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃo-LESS-key/) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations. == Statement == The Cholesky decomposition of a Hermitian positive-definite matrix...
0  Suppose the matrix is of the form $\tilde{A} = aI -A^TA$, where $I$ is the identity matrix and $a>eig(A^TA)$. Assume that Cholesky decomposition is possible. Do we get a nice analytic expression or low cost computation for Cholesky decomposition of $\tilde{A}$?

6  Suppose I have the Cholesky decomposition for a symmetric matrix $A$: $$A = L L^T$$ I wish to compute the Cholesky decomposition for $A+kI$ where $I$ is the identity and $k$ is a scalar. Is there a way to obtain this using the decomposition for $A$ faster than recomputing the Cholesky decompo...

13  I have a positive definite matrix $A$ ($n \times n$ dimension) for which I have the Cholesky decomposition $A=LL^{'}$. I want to use this to compute a) The Cholesky decomposition of $A+c^2\times I$ where $c$ is a constant and $I$ is the identity matrix b) The Cholesky decomposition of $A+BB^{... 15  When we have a symmetric matrix$A = LL^*$, we can obtain L using Cholesky decomposition of$A$($L^*$is$L$transposed). Can anyone tell me how we can get this same$L$using SVD or Eigen decomposition? Thank you. 8  Given a real Hermitian positive-definite matrix$A$is a decomposition of the form$A=L L^T\$ where L is a lower triangular matrix with positive diagonal entries. I read some proofs about the existence of Cholesky decomposition. Most of them start from LDU decomposition. Then the proof shows that ...

Queries which show also editors who added/removed the tag: data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/…