Browsing by Author "Ikramov K."

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  • A criterion for unitary congruence between complex matrices 
    Al'pin Y.; Ikramov K. (2012)
    Let A and B be square complex matrices of the same order n. Based on an important result Y. P. Hong and R. A. Horn, we propose a criterion for verifying unitary congruence of these matrices. The criterion requires that a ...
  • A criterion for unitary congruence between matrices 
    Al'pin Y.; Ikramov K. (2011)
    A criteria for unitary congruence between matrices is discussed. Matrices are proved to be unitarily congruent and thus the verification of unitary congruence between two matrices reduces to the condition of unitary ...
  • On condensed forms for partially commuting matrices 
    Alpin Y.; Elsner L.; Ikramov K. (2000)
    Two complex n×n matrices A and B are said to be partially commuting if A and B have a common eigenvector. We propose a condensed form for such matrices that can be obtained from A and B by a finite rational computation. ...
  • On the unitary similarity of matrix families 
    Al'pin Y.; Ikramov K. (2003)
    The classical Specht criterion for the unitary similarity between two complex n × n matrices is extended to the unitary similarity between two normal matrix sets of cardinality m. This property means that the algebra ...
  • Reducibility theorems for pairs of matrices as rational criteria 
    Al'pin Y.; Ikramov K. (2000)
    Theorems giving conditions for a pair of matrices to be reducible to a special form by a simultaneous similarity transformation such as the classical McCoy's theorem or theorems due to Shapiro and Watters are traditionally ...
  • Solving the two-dimensional CIS problem by a rational algorithm 
    Al'pin Y.; George A.; Ikramov K. (2000)
    The CIS problem is formulated as follows. Let p be a fixed integer, 1≤p<n. For given n×n compex matrices A and B, can one verify whether A and B have a common invariant subspace of dimension p by a procedure employing a ...
  • Unitary similarity of algebras generated by pairs of orthoprojectors 
    Al'pin Y.; Ikramov K. (2006)
    It is shown that the unitary similarity of two matrix algebras generated by pairs of orthoprojectors { P1, Q1} and {P 2,Q2} can be verified by comparing the traces of P 1, Q1, and (P1Q1)i, i = 1, 2, n, with those of P2, ...

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