## How do you calculate Lu in Matlab?

# How do you calculate Lu in Matlab?

## How do you calculate Lu in Matlab?

[ L , U ] = lu( A ) factorizes the full or sparse matrix A into an upper triangular matrix U and a permuted lower triangular matrix L such that A = L*U . [ L , U , P ] = lu( A ) also returns a permutation matrix P such that A = P’*L*U . With this syntax, L is unit lower triangular and U is upper triangular.

**How do you solve LU decomposition?**

LU Decomposition for Solving Linear Equations

- Describe the factorization A=LU A = L U .
- Compare the cost of LU with other operations such as matrix-matrix multiplication.
- Identify the problems with using LU factorization.
- Implement an LU decomposition algorithm.

**Is the LU factorization unique?**

(UT )−1 = (U−1)T ; the former is lower triangular and therefore the latter as well. the LU factorization is unique. LU factorization is not unique.

### What does Lu do in Matlab?

lu (MATLAB Functions) The lu function expresses a matrix X as the product of two essentially triangular matrices, one of them a permutation of a lower triangular matrix and the other an upper triangular matrix. The factorization is often called the LU, or sometimes the LR, factorization.

**Can you do LU factorization on a non square matrix?**

For matrices that are not square, LU decomposition still makes sense. Given an m × n matrix M, for example we could write M = LU with L a square lower unit triangular matrix, and U a rectangular matrix. Then L will be an m × m matrix, and U will be an m × n matrix (of the same shape as M).

**Does every matrix have an LU decomposition?**

Do matrices always have an LU decomposition? No. Sometimes it is impossible to write a matrix in the form “lower triangular”×“upper triangular”.

#### Does every invertible matrix have LU decomposition?

If the matrix is invertible (the determinant is not 0), then a pure LU decomposition exists only if the leading principal minors are not 0. If the matrix is not invertible (the determinant is 0), then we can’t know if there is a pure LU decomposition.

**Are there multiple LU decompositions?**

Existence and uniqueness cannot have an LU decomposition. The second negative result concerns uniqueness. Proposition If a matrix has an LU decomposition, then it is not unique.