The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2 × 2-matrix ring M2(R) and, if so, to compute such an embedding. We discuss many variants of this problem, including algorithmic recognition of quaternion algebras amo...

This article compares three different algorithms used to compute Euler angles from data obtained by the angular rate sensor (e.g., MEMS gyroscope)-the algorithms based on a rotational matrix, on transforming angular velocity to time derivations of the Euler angles and on unit quaternion expressing rotation. Algorithms are compared by their computational efficiency and accuracy of Euler angles e...

This paper proposes a novel robust digital color image watermarking algorithm which combines color image feature point extraction, shape image normalization and QPCA (quaternion principal component algorithm) basedwatermarking embedding (QWEMS) and extraction (QWEXS) schemes. The feature point extraction method called Mexican Hat wavelet scale interaction is used to select the points which can ...

Dupin cyclides are surfaces characterized by the property that all their curvature lines are circles or lines. Spheres, circular cylinders, cones and tori are particular examples. We introduce a bilinear rational Bézier-like formula with quaternion weights for parametrizing principal patches of Dupin cyclides. The proposed construction is not affine invariant but it is Möbius invariant, has low...

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. We show that the Fast Givens transformation, known for the real case, can also be defined for quaternion valued matrices, and we apply this technique to the r...