A Matrix Form of Taylor's Theorem
1930 ◽
Vol 2
(1)
◽
pp. 33-54
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Keyword(s):
The following pages continue a line of enquiry begun in a work On Differentiating a Matrix, (Proceedings of the Edinburgh Mathematical Society (2) 1 (1927), 111-128), which arose out of the Cayley operator , where xij is the ijth element of a square matrix [xij] of order n, and all n2 elements are taken as independent variables. The present work follows up the implications of Theorem III in the original, which stated thatwhere s (Xr) is the sum of the principal diagonal elements in the matrix Xr. This is now written ΩsXr = rXr – 1 and Ωs is taken as a fundamental operator analogous to ordinary differentiation, but applicable to matrices of any finite order n.
1932 ◽
Vol 3
(2)
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pp. 135-143
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Keyword(s):
1966 ◽
Vol 6
(4)
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pp. 512-512
1977 ◽
Vol 16
(3)
◽
pp. 361-369
2016 ◽
Vol 5
(2)
◽
pp. 13-25
1962 ◽
Vol 14
◽
pp. 553-564
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Keyword(s):
1997 ◽
Vol 3
(S2)
◽
pp. 957-958
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Keyword(s):
Keyword(s):
2021 ◽
Vol ahead-of-print
(ahead-of-print)
◽
Keyword(s):
Keyword(s):