R: Upper and Lower Triangular Matrixes

triang {fBasics} | R Documentation

## Upper and Lower Triangular Matrixes

### Description

Extracs the pper or lower tridiagonal part from a matrix.

### Usage

    triang(x)
    Triang(x)

### Arguments

`x` | a numeric matrix.

### Details

The functions `triang` and `Triang` allow to transform a square matrix to a lower or upper triangular form. A triangular matrix is either an upper triangular matrix or lower triangular matrix. For the first case all matrix elements `a[i,j]` of matrix `A` are zero for `i>j`, whereas in the second case we have just the opposite situation. A lower triangular matrix is sometimes also called left triangular. In fact, triangular matrices are so useful that much computational linear algebra begins with factoring or decomposing a general matrix or matrices into triangular form. Some matrix factorization methods are the Cholesky factorization and the LU-factorization. Even including the factorization step, enough later operations are typically avoided to yield an overall time savings. Triangular matrices have the following properties: the inverse of a triangular matrix is a triangular matrix, the product of two triangular matrices is a triangular matrix, the determinant of a triangular matrix is the product of the diagonal elements, the eigenvalues of a triangular matrix are the diagonal elements.

### References

Higham, N.J., (2002); Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM.

Golub, van Loan, (1996); Matrix Computations, 3rd edition. Johns Hopkins University Press.

### Examples

    ## Create Pascal Matrix:
       P = pascal(3)
       P

    ## Create lower triangle matrix
       L = triang(P)
       L

[Package fBasics version 3042.89 Index]