Titlebook: Geometric Multiplication of Vectors; An Introduction to G Miroslav Josipovi? Textbook 2019 Springer Nature Switzerland AG 2019 geometric (C

abandon

書目名稱Geometric Multiplication of Vectors影響因子(影響力)




書目名稱Geometric Multiplication of Vectors影響因子(影響力)學(xué)科排名




書目名稱Geometric Multiplication of Vectors網(wǎng)絡(luò)公開度




書目名稱Geometric Multiplication of Vectors網(wǎng)絡(luò)公開度學(xué)科排名




書目名稱Geometric Multiplication of Vectors被引頻次




書目名稱Geometric Multiplication of Vectors被引頻次學(xué)科排名




書目名稱Geometric Multiplication of Vectors年度引用




書目名稱Geometric Multiplication of Vectors年度引用學(xué)科排名




書目名稱Geometric Multiplication of Vectors讀者反饋




書目名稱Geometric Multiplication of Vectors讀者反饋學(xué)科排名

裝飾

無法治愈

Appendix,erefore, we can define the exponential function of the elements of a geometric algebra. In .3, we have four important types of elements (numbers): . (dual numbers, square to zero), . (square to ?1), . (square to 1), and . (square to itself). Nilpotents are the easiest to deal with: the expansion (?)

過分自信

小隔間

Euclidean 3D Geometric Algebra (,3),unit pseudoscalar . commutes with all elements of the algebra and squares to ?1, and therefore, it is an ideal replacement for the ordinary imaginary unit (there are many “imaginary units” in GA). A pseudoscalar with such properties will appear again in .7, .11, … (see E10). Here we often use a very useful form of a multivector:

殺死

Human Dignity as a Global Common GoodConsider two consecutive boosts in arbitrary directions and let us try to express them as a product of a boost and a rotation. For the hyperbolic sine and cosine we use the abbreviations . and ., while for the sine and cosine we use . and .. We have

殺死

https://doi.org/10.1007/978-981-97-6117-3We know how to multiply unit vectors; therefore, we can try to find some objects to . them. For vectors in .3, we need three parameters (three coordinates), and the geometric product is noncommutative. Consequently, we can choose matrices; 2?×?2 complex matrices will be enough. Matrices are a common choice for various representations.

Terrace

The Dirty, Working-Class Problem,Checking directly, we get .. Similarly, it is easy to obtain by a direct multiplication

Scleroderma

Applications,Consider two consecutive boosts in arbitrary directions and let us try to express them as a product of a boost and a rotation. For the hyperbolic sine and cosine we use the abbreviations . and ., while for the sine and cosine we use . and .. We have

切掉