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What is a sparse matrix ?

From: Henry F. Mollet
Subject: What is a sparse matrix ?
Date: Tue, 27 Apr 2004 16:00:16 -0700
User-agent: Microsoft-Entourage/

What is a sparse matrix? Is it a matrix with few elements (sparse?) and lots
of zeros? Can somebody please interpret the following description? Is a
Leslie matrix A (with matrix elements on the first row and first
sub-diagonal only and A = F + T) a sparse matrix?

The templated class sparse_matrix<T, F, A> is the base container adaptor for
sparse matrices. For a (m x n )-dimensional sparse matrix and 0 <= i < m ,0
<= j < n the non-zero elements mi, j are mapped via (i x n + j) for row
major orientation or via (i + j x m) for column major orientation to
consecutive elements of the associative container, i.e. for elements k=mi1,j
1and k + 1 = m i2,j 2of the container holds i1< i 2or (i 1= i 2and j1< j
2)with row major orientation or j1< j 2or (j 1= j 2and i1< i 2)with column
major orientation. 

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