Quaternions, due to their unique structure and properties, are a useful tool in quantum physics, robotics, modern computer science, and more. Quaternions are an example of a non-commutative division ring. This leads to interesting insights in the study of quaternionic matrices. A quick observation shows that, due to noncommutativity, many properties of quaternionic matrices that at first glance seem obvious actually require deeper consideration. In this work, we will examine the basic definitions and properties of quaternions and quaternionic matrices and compare them with complex matrices. We will explore an alternative definition of quaternions and its application in the study of matrix properties, and also touch upon the study of eigenvalues of these matrices.
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