# Questions tagged [matrix-decomposition]

Questions about matrix decompositions, such as the LU, Cholesky, SVD (Singular value decomposition) and eigenvalue-eigenvector decomposition.

1,432 questions
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### Using Cholesky decomposition to compute covariance matrix determinant

I am reading through this paper to try and code the model myself. The specifics of the paper don't matter, however in the authors matlab code I noticed they use a Cholesky decomposition instead of ...
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### What is the relevance of this theorem? (Complete orthogonal decomposition)

I'm reading the book Matrix Analysis for Scientists and Engineers by Alan J. Laub. In the chapter about Canonical forms, the following theorem is presented: Theorem 10.25 (Complete Orthogonal ...
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### Convergent series description of ratio of two bilinear forms

I have to numerically calculate the ratio of two bilinear forms: $\frac{x_1}{x_2} = \frac{v^T U_1 v}{v^T U_2 v}$, where $U_1$ and $U_2$ are unitary matrices. Both bilinear forms $x_1$ and $x_2$ are ...
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### Creating a correlated distribution with an indefinite matrix

For the past week, I've been trying to figure out how to implement a linear transformation of a random variable vector with entries $h_{i}$ of the form $\tilde h = Wh$ where h is a non correlated ...
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### Which type of factorization is appropriate?

I have a symmetric matrix (square)($A$) with positive values and zero on its main diagonal. I need to find a matrix $Y$ which is: $Y^TY = A$ I don't have any non-negativity constraint on the ...
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### What is the most general matrix that gives rise to all even characteristic polynomials?

Is there some general form of all matrices which give rise to all even or all odd characteristic polynomial terms? For skew-symmetric matrices such that $A^T=-A$ we necessarily have all even or all ...
### Is there any way to use matrix decomposition for finding $A^n$?
If I want to take the power of matrix $A$ with e.g 3, $A^3$ or with power of $-\frac {1}{2}$, e.g $A^{-\frac {1}{2}}$ etc. Is there an easy way to solve $A^n$, where $n\in R$ and $A \in R^{nxn}$ by ...