Description Usage Arguments Details References Examples

Extracs the pper or lower tridiagonal part from a matrix.

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`x` |
a numeric matrix. |

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.

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.

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

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