During synthesis of the discussed algorithm we use the fact that product of two biquaternions may be represented as a matrix鈥搗ector product. The matrix multiplicand that participates in the product calculating has unique structural properties that allow performing its advantageous factorization. ...
Makarov, O.M.: An algorithm for the multiplication of two quaternions. Zh. Vychisl. Mat. Mat. Fiz. 17(6), 1574–1575 (1977)MATH 8.Cariow, A., Cariowa, G.: Algorithm for multiplying two octonions. Radioelectronics and Communications Systems, pp. 464–473. Allerton Press, Inc., New...
The addition q1 + q2 and the multiplication q1 × q2 of two quaternions q1 and q2 are defined in a way similar to the one for complex numbers by taking into account the relations on i, j, k just mentioned. With evident notations, we obtain q1+q2=t1+t2+x1+x2i+y1+y2j+z1+z2k fo...
of Linear SystemsMatrix Multiplication by BlocksExplanation of the MethodThe Field of Complex NumbersAppendixAffine MapsThe Field of QuaternionsThe Strassen AlgorithmExercisesNotes Row by Column MultiplicationLinear Fractional TransformationsLinear Changes of VariablesDefinition of the Matrix ProductThe Map ...
In summary, my teacher was trying to explain to us that complex numbers in ℝ×ℝ can be thought of as plane with imaginary and real parts, and that the product of two complex numbers is the same as the magnitude of the real part multiplied by the angle between the real and ...
In fact, quaternions are an extension of complex numbers to four dimensions, since we can multiply two quaternions in a manner similar to the way that we can multiply two complex numbers. In this chapter, we are going to derive the formula for quaternion multiplication.Goldman, Ron...