Dual list
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2014-12-22 19:19:23 UTC.
- The original revision id was 535831376.
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Original Wikitext content:
If P is a matrix with rational coefficents, denote by Saturate(P) the integral matrix which is the [[saturation]] of P, defined in terms of the right reducing matrix to Smith normal form. We may clean the result up a little by LLL reduction, so let Sat(P) = LLL(Saturate(P)). Given an integral matrix A which we will view as a list of lists, A`A, where A` is the pseudoinverse of A, is the corresponding nxn projection matrix, where n. We may combine these two into the dual list function: Dulist(A) = Sat(I - A`A), where I is the identity matrix Supposing A is an integral matrix, A`A is
Original HTML content:
<html><head><title>dual list</title></head><body>If P is a matrix with rational coefficents, denote by Saturate(P) the integral matrix which is the <a class="wiki_link" href="/saturation">saturation</a> of P, defined in terms of the right reducing matrix to Smith normal form. We may clean the result up a little by LLL reduction, so let Sat(P) = LLL(Saturate(P)). Given an integral matrix A which we will view as a list of lists, A`A, where A` is the pseudoinverse of A, is the corresponding nxn projection matrix, where n. We may combine these two into the dual list function: Dulist(A) = Sat(I - A`A), where I is the identity matrix <br /> <br /> Supposing A is an integral matrix, A`A is</body></html>