# Questions tagged [matrix-decomposition]

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

1,443 questions
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### The benefit of LU decomposition over explicitly computing the inverse

I'm going to teach a linear algebra course in the fall, and I want to motivate the topic of matrix factorizations such as the LU decomposition. A natural question one can ask is, why care about this ...
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### null space from SVD

It is said that a matrix's null space can be derived from QR or SVD. I tried an example: $$A= \begin{bmatrix} 1&3\\ 1&2\\ 1&-1\\ 2&1\\ \end{bmatrix}$$ I'm convinced that QR (more ...
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### Most efficient method for computing Singular Value Decomposition of a triangular matrix?

There are several methods available for computing SVD of a general matrix. I am interested in knowing about the best approach which could be used for computing SVD of an upper triangular matrix. ...
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### Cholesky of Matrix plus Identity

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 $A+c^2\times I$ ...
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### A criteria for Jordan decomposition of a matrix over a general ring

When I look at different proofs of the Jordan-Chevalley decomposition of a matrix, the minimal hypothesis I usually found is about the perfection of the field over which such decomposition occurs (e.g....
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### Determinant of matrix with binomial coefficients entries

I try that find the way for calculate the determinant of the following matrix of size $n\times n$. The determinant is $\displaystyle\binom{k+n}{k}x^{n}$. I wait that you can help me. THE OMITTED ...
### Solving the matrix equation $X^tA+A^tX=0$ for $X$ in terms of $A$
Suppose that I know $A$. And all matrices in the equation are square matrices. I want to solve for $X$ given that $$X^tA + A^tX = 0$$ I'm not really good at matrix calculus. Is it possible to solve ...