## How do you find 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 use LU command in Matlab?

[L,U,p,q,R] = lu( A , ‘vector’ ) returns the permutation information in two row vectors p and q , such that R(:,p)\A(:,q) = L*U . lu( A ) returns the matrix that contains the strictly lower triangular matrix L (the matrix without its unit diagonal) and the upper triangular matrix U as submatrices.

**How do you find the eigenvalues of a matrix in Matlab?**

e = eig( A ) returns a column vector containing the eigenvalues of square matrix A . [ V , D ] = eig( A ) returns diagonal matrix D of eigenvalues and matrix V whose columns are the corresponding right eigenvectors, so that A*V = V*D .

**What is permutation matrix in LU decomposition?**

It is also referred to as the LU factorization with Partial Pivoting (LUP) with row permutations only. An LU factorization with full pivoting involves both row and column permutations, PAQ=LU, P A Q = L U , where L and U, and P are defined as before, and Q is a permutation matrix that reorders the columns of A.

### How do you find the eigenvalues of a matrix?

In order to find eigenvalues of a matrix, following steps are to followed:

- Step 1: Make sure the given matrix A is a square matrix.
- Step 2: Estimate the matrix.
- Step 3: Find the determinant of matrix.
- Step 4: From the equation thus obtained, calculate all the possible values of.
- Example 2: Find the eigenvalues of.

### How do you prove that Lu is unique?

Theorem: If an upper triangular matrix U can be produced by Gauss elimination from a matrix A (i.e., no 0 diagonal elements are encountered) in the process, then A has a unique factorization in the form A = LU, where L is a low triangular matrix with all 1’s in the diagonal.