chapGPT 真神了

[Caravel]

What is SO(3) in physics？
答：In physics, the special orthogonal group SO(3) is the group of rotations in three-dimensional space. It consists of all the rotations about the origin that preserve the length of vectors and the orientation of an orthonormal basis.

SO(3) is a continuous group, meaning that it is a group of transformations that can be continuously parameterized by real numbers. The elements of SO(3) can be represented by 3x3 matrices that satisfy certain conditions, and the group operation is matrix multiplication.

In physics, the group SO(3) is important because it is a symmetry group, meaning that it consists of transformations that leave the laws of physics invariant. For example, the laws of physics are the same for an observer who is rotating about the origin as for one who is not rotating. The group SO(3) is used to classify and study the symmetries of physical systems.

SO(3) also has applications in other areas of mathematics, such as geometry and topology, as well as in other fields, such as engineering and computer science.


Can SO(3) have 9 dimension representation?

Yes, it is possible for the special orthogonal group SO(3), which consists of rotations in three-dimensional space, to have a nine-dimensional representation.

In general, a group representation is a group homomorphism from a group to the group of invertible linear transformations of a vector space. The dimension of a representation is equal to the dimension of the vector space on which the group is acting.

So, a nine-dimensional representation of SO(3) would map each element of the group to a 9x9 matrix that represents a linear transformation of a nine-dimensional vector space. This representation would be higher-dimensional than the defining representation of SO(3), which is a three-dimensional representation that maps each element of the group to a 3x3 matrix that represents a rotation in three-dimensional space.

Higher-dimensional representations of SO(3) can be useful for studying the symmetries of physical systems, as well as for other applications in mathematics and other fields. However, the interpretation of the elements of these higher-dimensional representations in terms of rotations in three-dimensional space may not be as straightforward as in the defining representation.

以后学习之前要问问chatGPT

[TheMatrix]

What is SO(3) in physics？
答：In physics, the special orthogonal group SO(3) is the group of rotations in three-dimensional space. It consists of all the rotations about the origin that preserve the length of vectors and the orientation of an orthonormal basis.

SO(3) is a continuous group, meaning that it is a group of transformations that can be continuously parameterized by real numbers. The elements of SO(3) can be represented by 3x3 matrices that satisfy certain conditions, and the group operation is matrix multiplication.

In physics, the group SO(3) is important because it is a symmetry group, meaning that it consists of transformations that leave the laws of physics invariant. For example, the laws of physics are the same for an observer who is rotating about the origin as for one who is not rotating. The group SO(3) is used to classify and study the symmetries of physical systems.

SO(3) also has applications in other areas of mathematics, such as geometry and topology, as well as in other fields, such as engineering and computer science.


Can SO(3) have 9 dimension representation?

Yes, it is possible for the special orthogonal group SO(3), which consists of rotations in three-dimensional space, to have a nine-dimensional representation.

In general, a group representation is a group homomorphism from a group to the group of invertible linear transformations of a vector space. The dimension of a representation is equal to the dimension of the vector space on which the group is acting.

So, a nine-dimensional representation of SO(3) would map each element of the group to a 9x9 matrix that represents a linear transformation of a nine-dimensional vector space. This representation would be higher-dimensional than the defining representation of SO(3), which is a three-dimensional representation that maps each element of the group to a 3x3 matrix that represents a rotation in three-dimensional space.

Higher-dimensional representations of SO(3) can be useful for studying the symmetries of physical systems, as well as for other applications in mathematics and other fields. However, the interpretation of the elements of these higher-dimensional representations in terms of rotations in three-dimensional space may not be as straightforward as in the defining representation.

以后学习之前要问问chatGPT

可以替代一部分wiki的功能了。

[fhnan]

今天我问chatgpt美国众议院现任议长是谁， 它说现在，美国众议院议长是卡尔·科尔伯格。他于2021年1月3日就职。 我都不知道它这个答案是哪里来的

[TheMatrix]

今天我问chatgpt美国众议院现任议长是谁， 它说现在，美国众议院议长是卡尔·科尔伯格。他于2021年1月3日就职。 我都不知道它这个答案是哪里来的

你可以说“你错了，重新去查”，它会再给你一个答案。

[Caravel]

chatgpt 这个水平可以挣钱了，最先替代的应该是一部分文秘工作，比如律师看材料直接可以让它先看，看完，律师提问

[verdelite]

chatgpt 这个水平可以挣钱了，最先替代的应该是一部分文秘工作，比如律师看材料直接可以让它先看，看完，律师提问

完了，我同事已经用它来干工作了。具体来说，是写程序。一些小的具体的任务，让它写。写完了人工看一遍稍微改改，就行了。真是又快又好。