# ON REDUCTION OF K-ALMOST NORMAL AND K-ALMOST CONJUGATE NORMAL MATRICES TO A BLOCK TRIDIAGONAL FORM

• ASIL, K. NIAZI (DEPARTMENT OF MATHEMATICS, LORESTAN UNIVERSITY) ;
• KAMALVAND, M. GHASEMI (DEPARTMENT OF MATHEMATICS, LORESTAN UNIVERSITY)
• Accepted : 2019.09.11
• Published : 2019.09.25

#### Abstract

This paper examines how one can build a block tridiagonal structure for k-almost normal matrices and also for k-almost conjugate normal matrices. We shall see that these representations are created by unitary similarity and unitary congruance transformations, respectively. It shall be proven that the orders of diagonal blocks are 1, k + 2, 2k + 3, ${\ldots}$, in both cases. Then these block tridiagonal structures shall be reviewed for the cases where the mentioned matrices satisfy in a second-degree polynomial. Finally, for these processes, algorithms are presented.

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