Triangular Matrix
An upper triangular matrix 
is defined by
 |
(1) |
Written explicitly,
![U=[a_(11) a_(12) ... a_(1n); 0 a_(22) ... a_(2n); | | ... |; 0 0 ... a_(nn)].](https://mathworld.wolfram.com/images/equations/TriangularMatrix/NumberedEquation2.svg) |
(2) |
A lower triangular matrix 
is defined by
 |
(3) |
Written explicitly,
![L=[a_(11) 0 ... 0; a_(21) a_(22) ... 0; | | ... 0; a_(n1) a_(n2) ... a_(nn)].](https://mathworld.wolfram.com/images/equations/TriangularMatrix/NumberedEquation4.svg) |
(4) |
See also
Hankel Matrix, Hessenberg Matrix, Hilbert Matrix, Lower Triangular Matrix, Matrix, Strictly Lower Triangular Matrix, Strictly Upper Triangular Matrix, Upper Triangular Matrix, Vandermonde 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
Cite this as:
Weisstein, Eric W. "Triangular Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TriangularMatrix.html