矩阵的三角分解是求解线性方程组常用的方法，包括LU分解，LDU分解，杜利特(Doolittle)分解，克劳特(Crout)分解，LLT(乔累斯基Cholesky)分解，LDLT(不带平方根乔累斯基)分解等，以及为了满足分解条件又加入行列变换的LPU分解，PLU分解，LUP分解，LDPU分解等。

$$ A = LDU = E^{-1} \begin{bmatrix}1&0&0\\0&2&0\\0&0&2\end{bmatrix} \begin{bmatrix}1&0&1\\0&1&0\\0&0&1\end{bmatrix} $$

This calculator uses Wedderburn rank reduction to find the LDU factorization of a matrix $A$. The process constructs the three matrices $L$, $D$, $U$ in stages. $L$ is constructed a column at …

2020年7月5日 · 5.6. LU and LDU Factorizations 2 Example 5.6.A. The proof of Theorem 5.6.A gives the algorithm by which the LU-factorization of an appropriate matrix can be found. We row reduce A to row echelon form U and, as each elementary row operation is performed in the reduction of A, perform the inverse of that operation to the identity matrix to ...

An overview of LDU factorization and examples in Linear Algebra

Find the LDU factorization of A = [ - 3 1 2 9 1 2 - 5 3 - 2 1 - 1 5 5 0 7 4 ] That is , write A = LDU where L is a lower triangular matrix with ones on the diagonal, D is a diagonal matrix, and U is an upper triangular matrix with ones on the

2024年11月1日 · Find LDU-decomposition of the matrix A = 2 1 0 0 0 1 2 1 0 0 0 1 2 1 0 0 0 1 2 1 0 0 0 1 2 . Solution: We run Gauss elimination to produce the upper triangular matrix DU. Also, notice that the matrix A is symmetric, so the LDU-decomposition is actually LDL ⊤ …

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