You can imagine that if a vector is viewed from an angle, then its components will vary with the perspective.

你可以想象一下,如果换一个角度观察矢量,其分量会相应地发生变化

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If I just come and say to you, "Here's the vector whose components are 3 and 5.

假如我问你们,"一个矢量的分量分别是 3 和 5

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So the components of the vector are not invariant characterizations of the vector.

矢量的两个分量,并不是一成不变的

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The components of the vector are not the same.

矢量的分量和原来的也不再相同

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So the components of vector are not invariant.

因此矢量的分量不是一成不变的

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If you do, the unit vectors are called i prime and j prime, the components of the vector change.

如果这么做,单位矢量就是 i' 和 j',矢量的两个分量也会发生变化

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It's not enough to say these are the components of the vector; you've got to tell me, "I am working with i and j, which I define in the following manner."

所以,只说"这些是某矢量的分量"是不够的,你还得告诉我,"我选取的基矢是 i 和 j,它们是这样定义的"

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Now, when you work with components, Ax and Ay, if I didn't mention it, they are the components of the vector, you can do all your bookkeeping in terms of Ax and Ay.

当你们在计算分量 Ax 和 Ay 的时候,即使我没有说明,你们也要记得它们是矢量的分量,你们可以都用 Ax 和 Ay 的形式来表示

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I gave you a law of transformation of the components; namely, if the vector has components Ax and Ay in one reference frame and Ax prime and Ay prime in another reference frame, how are the two related?

我介绍过分量变换的法则,即如果矢量在一个坐标系的分量为 Ax 和 Ay,在另一坐标系中的分量为 Ax' 与 Ay',它们有着什么样的联系

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