Tuesday, May 15, 2012

Upper Triangular Matrix

A triangular matrix U of the form
 U_(ij)={a_(ij)   for i<=j; 0   for i>j.
(1)
Written explicitly,
 U=[a_(11) a_(12) ... a_(1n); 0 a_(22) ... a_(2n); | | ... |; 0 0 ... a_(nn)].
(2)
An upper triangular matrix with elements f[i,j] above the diagonal could be formed in versions of Mathematica prior to 6 using UpperDiagonalMatrix[f, n], which could be run after first loading LinearAlgebra`MatrixManipulation`.
A strictly upper triangular matrix is an upper triangular matrix having 0s along the diagonal as well, i.e., a_(ij)=0 for i>=j.

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