“quaternion”的概念、定义、翻译、参考文献-科学参考

quaternion

Physics

Symbol Q. A mathematical quantity defined by Q=a + bi + cj + dk, where a, b, c, and d are real numbers and i, j, and k are unit vectors in the x, y, and z directions, respectively. Quaternions were invented by Sir William Hamilton in 1843 and have been used extensively in physics, especially for problems involving rotation. Quaternions have close connections with the way in which spin is analysed in quantum mechanics and supersymmetry.

Mathematics

The complex number system can be obtained by taking a complex number to be an expression a + bi, where a and b are real numbers, and defining addition and multiplication in the natural way with the understanding that i² = −1. In an extension of this idea, Hamilton introduced the following notion, originally for use in mechanics. Define a quaternion to be an expression a + bi + cj + dk, where a, b, c, and d are real numbers, and define addition and multiplication in the natural way, with

$i^{2} = j^{2} = k^{2} = - 1, i j = - j i = k, j k = - k j = i, k i = - i k = j .$

All the normal laws of algebra hold except that multiplication is not commutative. That is to say, the quaternions form a division ring. See also division algebra.

单词	quaternion
释义	quaternion Physics Symbol Q. A mathematical quantity defined by Q=a + bi + cj + dk, where a, b, c, and d are real numbers and i, j, and k are unit vectors in the x, y, and z directions, respectively. Quaternions were invented by Sir William Hamilton in 1843 and have been used extensively in physics, especially for problems involving rotation. Quaternions have close connections with the way in which spin is analysed in quantum mechanics and supersymmetry. Mathematics The complex number system can be obtained by taking a complex number to be an expression a + bi, where a and b are real numbers, and defining addition and multiplication in the natural way with the understanding that i² = −1. In an extension of this idea, Hamilton introduced the following notion, originally for use in mechanics. Define a quaternion to be an expression a + bi + cj + dk, where a, b, c, and d are real numbers, and define addition and multiplication in the natural way, with $i^{2} = j^{2} = k^{2} = - 1, i j = - j i = k, j k = - k j = i, k i = - i k = j .$ All the normal laws of algebra hold except that multiplication is not commutative. That is to say, the quaternions form a division ring. See also division algebra.
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