Displaying similar documents to “Commutative/noncommutative rank of linear matrices and subspaces of matrices of low rank.”

A New Characterization of Generalized Complementary Basic Matrices

Miroslav Fiedler, Frank J. Hall (2014)

Special Matrices

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In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases

Linear Map of Matrices

Karol Pąk (2008)

Formalized Mathematics

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The paper is concerned with a generalization of concepts introduced in [13], i.e. introduced are matrices of linear transformations over a finitedimensional vector space. Introduced are linear transformations over a finitedimensional vector space depending on a given matrix of the transformation. Finally, I prove that the rank of linear transformations over a finite-dimensional vector space is the same as the rank of the matrix of that transformation.