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.
Baliarsingh, P., & Dutta, S. (2015). On an explicit formula for inverse of triangular matrices. Journal of the Egyptian Mathematical Society, 23(2), 297-302. doi: 10.1016/j.joems.2014.06.001
MLA
Pinakadhar Baliarsingh; Salila Dutta. "On an explicit formula for inverse of triangular matrices", Journal of the Egyptian Mathematical Society, 23, 2, 2015, 297-302. doi: 10.1016/j.joems.2014.06.001
HARVARD
Baliarsingh, P., Dutta, S. (2015). 'On an explicit formula for inverse of triangular matrices', Journal of the Egyptian Mathematical Society, 23(2), pp. 297-302. doi: 10.1016/j.joems.2014.06.001
VANCOUVER
Baliarsingh, P., Dutta, S. On an explicit formula for inverse of triangular matrices. Journal of the Egyptian Mathematical Society, 2015; 23(2): 297-302. doi: 10.1016/j.joems.2014.06.001
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