Movatterモバイル変換

TOPICS

Triangular Matrix

Anupper 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)

Alower 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

Explore with Wolfram|Alpha

More things to try:

References

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

Referenced on Wolfram|Alpha

Triangular Matrix

Cite this as:

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

Subject classifications

Created, developed and nurtured by Eric Weisstein at Wolfram Research

[8]ページ先頭

©2009-2025 Movatter.jp