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GeezerVison is showing mathworld.wolfram.com — Upper Triangular Matrix -- from Wolfram MathWorld

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Upper Triangular Matrix

An upper triangular matrix is 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)

A matrix m can be tested to determine if it is upper triangular in the Wolfram Language using UpperTriangularMatrixQ[m].

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.

See also

Lower Triangular Matrix, Strictly Upper Triangular Matrix, Triangular Matrix

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References

Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 10, 1962.

Referenced on Wolfram|Alpha

Upper Triangular Matrix

Cite this as:

Weisstein, Eric W. "Upper Triangular Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UpperTriangularMatrix.html

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