Row and Column Inclusion and the Distribution of Rank
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This chapter contains a detailed account of the distribution of rank deficient submatrices within a TN matrix, including a discussion of the important notion of row and column inclusion. The distribution of ranks among submatrices of a TN matrix is much less free than in a general matrix. Rank deficiency of submatrices in certain positions requires rank deficiency elsewhere. Whereas, in the case of general matrices, rank deficiency of a large submatrix can imply rank deficiency of smaller, included submatrices, in the TN case rank deficiency of small submatrices can imply that of much larger ones. The chapter discusses this and other related phenomenon.
1977 ◽
Vol 38
(03)
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pp. 0640-0651
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2020 ◽
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2017 ◽
2017 ◽
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2017 ◽
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