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A077606
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Left differencing matrix, D, by antidiagonals.
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1
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1, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,1
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COMMENTS
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If v is a sequence written as a column vector, then Dv is the sequence of first differences of v. The inverse of D is the left summing matrix; the transpose of D is the right differencing matrix.
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LINKS
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FORMULA
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D(n, n-1)=-1, D(n, n)=1, else D(n, k)=0.
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EXAMPLE
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Northwest corner:
1 0 0 0 0
-1 1 0 0 0
0 -1 1 0 0
0 0 -1 1 0
0 0 0 -1 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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