Titlebook: Linear Algebra and Group Theory for Physicists and Engineers; Yair Shapira Textbook 20191st edition Springer Nature Switzerland AG 2019 Gr

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Springer Nature Switzerland AG 2019

开始发作

Vector Product with Applications in Geometrical MechanicsHow to use vectors and matrices? Well, we’ve already seen a few important applications: the sine, cosine, and Fourier transforms. Here, on the other hand, we use matrices and their determinant to introduce yet another practical operation: vector product in 3-D.

疏忽

Special Relativity: Algebraic Point of ViewTo model static shapes in the plane, the ancient Greeks introduced Euclidean geometry. To model motion, on the other hand, Newton added a new time axis, perpendicular to the plane. This may help model a force, applied to an object from the outside to accelerate its original motion.

去世

Group Representation and Isomorphism TheoremsWhat is the most elementary algebraic object? This could be the individual number. In the previous part, we also introduced more complicated algebraic structures: vectors and matrices.

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Projective Geometry with Applications in Computer GraphicsWhat is a geometrical object?It is something that we humans could imagine and visualize. Still, in Euclidean geometry, a geometrical object is never defined explicitly, but only implicitly, in terms of relations, axioms, and logic ([22] and Chap. 6 in [63]).

人类的发源

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赦免

Automatic Mesh GenerationConsider a complicated domain in three spatial dimensions. How to store it on the computer? For this purpose, it must be discretized: approximated by a discrete mesh, ready to be used in practical algorithms.