matrix-triang: Upper and Lower Triangular Matrixes

Description Usage Arguments Details References Examples

Description

Extracs the pper or lower tridiagonal part from a matrix.

Usage

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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

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## Create Pascal Matrix:
   P = pascal(3)
   P
   
## Create lower triangle matrix
   L = triang(P)
   L                                

fBasics documentation built on Nov. 18, 2017, 4:05 a.m.