On an explicit formula for inverse of triangular matrices
Baliarsingh, P., Dutta, S. (2015). On an explicit formula for inverse of triangular matrices. EKB Journal Management System, 23(2), 297-302. doi: 10.1016/j.joems.2014.06.001
Pinakadhar Baliarsingh; Salila Dutta. "On an explicit formula for inverse of triangular matrices". EKB Journal Management System, 23, 2, 2015, 297-302. doi: 10.1016/j.joems.2014.06.001
Baliarsingh, P., Dutta, S. (2015). 'On an explicit formula for inverse of triangular matrices', EKB Journal Management System, 23(2), pp. 297-302. doi: 10.1016/j.joems.2014.06.001
Baliarsingh, P., Dutta, S. On an explicit formula for inverse of triangular matrices. EKB Journal Management System, 2015; 23(2): 297-302. doi: 10.1016/j.joems.2014.06.001

On an explicit formula for inverse of triangular matrices

Journal of the Egyptian Mathematical Society
Volume 23, Issue 2, 2015, Page 297-302  XML PDF (433.68 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.06.001
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Authors
Pinakadhar Baliarsingh* 1; Salila Dutta2
1Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar 751024, India
2Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, India
Abstract
In the present article, we define difference operators BLða½mÞ and BUða½mÞ which represent a lower triangular and upper triangular infinite matrices, respectively. In fact, the operators
BLða½mÞ and BUða½mÞ are defined by ðBLða½mÞxÞk ¼ Pm
i¼0akiðiÞxki and ðBUða½mÞxÞk
¼ Pm
i¼0akþiðiÞxkþi for all k; m 2 N0 ¼ f0; 1; 2; 3; ...g, where a½m¼fað0Þ; að1Þ; ... aðmÞg, the set of
convergent sequences aðiÞ¼ðakðiÞÞk2N0
ð0 6 i 6 mÞ of real numbers. Indeed, under different limiting
conditions, both the operators unify most of the difference operators defined by various triangles
such as D;Dð1Þ
;Dm;DðmÞ
ðm 2 N0Þ;Da
;DðaÞ
ða 2 RÞ; Bðr;sÞ;Bðr;s;tÞ;Bðr~;s~;t
~; u~Þ, and many others.
Also, we derive an alternative method for finding the inverse of infinite matrices BLða½mÞ and
BUða½mÞ and as an application of it we implement this idea to obtain the inverse of triangular
matrices with finite support. 
Keywords
Difference operators BLða½mÞ and BUða½mÞ; Cesa`ro mean operator; Riesz mean and generalized mean operator
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