Survey of Modern Algebr: The system of quaternions. Follow the step to talk about the essay.

Survey of Modern Algebr: The system of quaternions. Follow the step to talk about the essay..

I need an explanation for this Mathematics question to help me study.

The system of quaternions was discovered by William Rowan Hamilton on the afternoon of Monday, October 16, 1843, as he walked along Royal Canal in Dublin. A quaternion is an abstract symbol of the form a + bi + cj + dk, where a, b, c, d R are real numbers: H = {a + bi + cj + dk : a, b, c, d in R. The “imaginary units” i,j, k are abstract symbols satisfying the following multiplication rules: i^2+j^2+ k^2 = ijk=1. One can check that {H, +, *, 0, 1} is a ring. However, it is not a commutative ring because (for example) we have ij =-k and ji=-k not eaqual k. Your assignment is to write a mathematical paper about the quaternions, including some of exposition and history, but focusing mainly on mathematical results. Here are some ideas:

Survey of Modern Algebr: The system of quaternions. Follow the step to talk about the essay.

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