Results 1 to 10 of about 251 (42)
Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
Special Matrices, 2014 L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331(2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformationsA ↦ ˜S−1AS in which S is a nonsingular quaternion matrix ...
Klimchuk Tatiana, Sergeichuk Vladimir V.
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W-MPD–N-DMP-solutions of constrained quaternion matrix equations
Special Matrices, 2023 The solvability of several new constrained quaternion matrix equations is investigated, and their unique solutions are presented in terms of the weighted MPD inverse and weighted DMP inverse of suitable matrices.
Kyrchei Ivan I. +2 more
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The explicit formula for Gauss-Jordan elimination applied to flexible systems
Special Matrices, 2022 Flexible systems are obtained from systems of linear equations by adding to the elements of the coefficient matrix and the right-hand side scalar neutrices, which are convex groups of (non-standard) real numbers.
Tran Nam Van +2 more
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Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices
Open Mathematics, 2021 In this paper, the authors extend determinantal inequalities of the Hua-Marcus-Zhang type for positive definite matrices to the corresponding ones for quaternion matrices.
Hong Yan, Qi Feng
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Singular matrices that are products of two idempotents or products of two nilpotents
Special Matrices, 2021 Over commutative domains we characterize the singular 2 × 2 matrices which are products of two idempotents or products of two nilpotents. The relevant casees are the matrices with zero second row and the singular matrices with only nonzero entries.
Călugăreanu Grigore
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On idempotent stable range 1 matrices
Special Matrices, 2022 We characterize the idempotent stable range 1, 2 × 2 matrices over commutative rings and in particular the integral matrices with this property. Several special cases and examples complete the subject.
Călugăreanu Grigore, Pop Horia F.
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Determinants of some special matrices over commutative finite chain rings
Special Matrices, 2020 Circulant matrices over finite fields and over commutative finite chain rings have been of interest due to their nice algebraic structures and wide applications. In many cases, such matrices over rings have a closed connection with diagonal matrices over
Jitman Somphong
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Journal of Mathematical Cryptology, 2022 Rahman and Shpilrain proposed a Diffie–Hellman style key exchange based on a semidirect product of n×nn\times n-matrices over a finite field. We show that, using public information, an adversary can recover the agreed upon secret key by solving a system ...
Brown Daniel R. L. +2 more
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Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields
Special Matrices, 2021 The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽n×n is defined as ℓ1ℓ2· · · ℓn, where ℓj ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero ...
Dukes Peter J., Martínez-Rivera Xavier
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Factorization of Matrices of Quaternions [PDF]
, 2012 We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization.
Loring, Terry A.
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