column space


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column space

[′käl·əm ‚spās]
(mathematics)
The vector space spanned by the columns of a matrix.
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sparse column space basis, sparse null space basis, block angular matrix, block diagonal matrix, matching, hypergraph partitioning, inverse of a basis
We describe new approaches for obtaining an implicit null space basis by computing a basis for the column space of A; the matrix representing the column space basis is required to have a sparse inverse.
The motivation for our work is to obtain a different implicit representation of a null space basis by computing a column space basis B that has a sparse inverse.
Our approach in this paper is to select a basis B that has a block angular form for the column space of the matrix A.
In some applications a sparse inverse for the column space basis, [B.
We take two approaches to design algorithms for computing bases with sparse inverses for the column space.
In Section 3, we describe heuristic greedy algorithms for computing column space bases with sparse inverses by means of matchings in bipartite graphs.
Recall that the choice of a column space basis B immediately determines a fundamental null space basis Z in terms of B and the submatrix N formed by columns of A outside the basis.
Why is he allowed so much column space for his insular ramblings?
If the Games are as dull as you reckon, why waste column space telling us?
The bottom tension chords doubled as the first supporting steel floor above the highway providing a totally free column space floor.