# Questions tagged [lu-decomposition]

The tag has no usage guidance.

60 questions
4answers
5k views

### Is the $L$ in $LU$ factorization unique?

I was doing an $LU$ factorization problem \begin{bmatrix} 2 & 3 & 2 \\ 4 & 13 & 9 \\ -6 & 5 &4 \end{bmatrix} and I was going to multiply the second row by ...
1answer
1k views

### Cholesky decomposition when deleting one row and one and column.

I've thought about this problem for days but could not find a good answer. Given Cholesky decomposition of a symmetric positive semidefinite matrix $A = LL^T$. Now, suppose that we delete the $i$-th ...
1answer
885 views

### Complexity/Operation count for the forward and backward substitution in the LU decomposition?

If I have a linear system of equations $Ax=b$ where $A \in \mathbb{R} ^{n\times n}, x \in \mathbb{R} ^{n}, b \in \mathbb{R} ^{n}$ this system can be solved for $x$ via an LU decomposition: $$A = LU$$ ...
2answers
514 views

### LU-decomposition of A

I have: $A=\begin{bmatrix} 2 & -1 & 2 & 3 & 4 \\ 4 & -2 & 7 & 7 & 6 \\ 2 & -1 & 20 & 9 & -8 \end{bmatrix}$ and I'm asked to LU-decomposition A, then ...
2answers
43 views

### 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 ...
1answer
79 views

### Which one is most cost expensive to solve a linear equation? LU or inverse?

Which one is the most expensive way to solve for linear equation? LU-decomposition $$A = LU$$ Or finding the inverse $$A^{-1} = \frac{1}{\det(A)} \operatorname{adj}(A)$$ If I have to choose, I ...
1answer
4k views

1answer
464 views

### LU decomposition without pivoting for symmetric definite negative matrix?

While studying LU decomposition from this book I came across the statement that pivoting in LU decomposition is not necessary in some cases, as for example when the matrix is symmetric positive ...
2answers
156 views

### Factorization of matrices over GF$(2)$

Suppose $A\in \mathbb{F}_2^{n\times n}$ is full rank non-symmetric matrix. Then, can we write $A=BB^T$ for some full-rank $B$? I know there exists a Cholesky factorization, but its not clear if that ...
1answer
41 views

### How can I find the pivot matrix from LU-factorization?

I trying to solve LU-factrization with pivoting: $$PA=LU$$ By using the subroutine sgeft2 from Lapack. It's a Fortran 90 library for numerical linear algebra. I have found the $L$ and $U$ matrix, ...
2answers
46 views

### I want to know $PA=LU$ , what is $P$??

I know that if there is a $0$ in the diagonal, I use multiply $P$ to $A$. But, I saw the use of $P$ even if there was no zero. I want to know what $P$ is and what role it is for.
1answer
51 views