Triangular Matrix

An upper triangular matrix is defined by

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

(1)

Written explicitly,

U=[a_(11) a_(12) ... a_(1n); 0 a_(22) ... a_(2n); | | ... |; 0 0 ... a_(nn)].

(2)

A lower triangular matrix is defined by

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

(3)

Written explicitly,

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

(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.

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Triangular Matrix

Cite this as:

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

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