Lower Triangular Matrix

A triangular matrix L of the form

 L_(ij)={a_(ij)   for i>=j; 0   for i<j.

Written explicitly,

 L=[a_(11) 0 ... 0; a_(21) a_(22) ... 0; | | ... 0; a_(n1) a_(n2) ... a_(nn)].

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

A strictly lower triangular matrix is a lower triangular matrix having 0s along the diagonal as well, i.e., a_(ij)=0 for i<=j.

See also

Strictly Lower Triangular Matrix, Triangular Matrix, Upper Triangular Matrix

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

Referenced on Wolfram|Alpha

Lower Triangular Matrix

Cite this as:

Weisstein, Eric W. "Lower Triangular Matrix." From MathWorld--A Wolfram Web Resource.

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