4 citations · 6 across the 9 of their papers we have counts for
9 papers
Recursive construction of spectral basis and its application to matrices
A. Acus, A. Dargys
We prove a recursive formula for construction of generalized spectral basis. Example of application is presented for symbolic computation with non-diagonalizable matrix that descri…
Square roots of complexified quaternions
Adolfas Dargys, Arturas Acus
Square roots of complexified (complex) quaternions, namely, the Hamilton quaternion, coquaternion, nectorine, and conectorine are investigated. The isomorphisms between the complex…
Spectral square roots of the multivector
Adolfas Dargys, Arturas Acus
The problem of multivector (MV) multiple square roots in real geometric Clifford algebras Cl(p,q) with symbolic coefficients is considered. The method to find multiple MV square ro…
Clifford geometric algebra: Real and complex spinor data tables
A. Acus, A. Dargys
The modern algebra concepts are used to construct tables of algebraic spinors related to Clifford algebra multivectors with real and complex coefficients. The following data comput…
Multivector (MV) functions in Clifford algebras of arbitrary dimension: Defective MV case
A. Acus, A. Dargys
Explicit formulas to calculate MV functions in a basis-free representation are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on analysis of…
Coordinate-free exponentials of general multivector (MV) in Cl(p,q) algebras for p+q=3
A. Acus, A. Dargys
Closed form expressions in a coordinate-free form in real Clifford geometric algebras (GAs) Cl(0,3), Cl(3,0)$, Cl(1,2) and Cl(2,1) are found for exponential function when the expon…
Exponentials of general multivector (MV) in 3D Clifford algebras
Adolfas Dargys, Arturas Acus
Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Cl(p,q) are presented for n=p+q=3. The obtained exponential…
Square root of a multivector of Clifford algebras in 3D: A game with signs
A. Acus, A. Dargys
An algorithm to extract the square root in radicals from a multivector (MV) in real Clifford algebras Cl(p,q) for n=p+q <=3 is presented. We show that in the algebras Cl(3,0), Cl(1…
Pseudospin, velocity and Berry phase in a bilayer graphene
Adolfas Dargys, Arturas Acus
Hamiltonian and eigenstate problem is formulated for a bilayer graphene in terms of Clifford's geometric algebra \textit{Cl}. It is shown that such approach allows to perfo…