Vectors: alternative definitions

[last updated: 2024-03-10]
vectors

(link to:) Vectors - wikipedia
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This page is incomplete/unfinished ...

• a set of numbers that "transform properly" when you change coordinates (Grifiths)
  It seems to me this definition is unnecessarily convoluted, introducing a new semi-undefined property, that being "proper transform",
  and it would be sufficient to just say that the numbers must be referencing some coordinate system.
  The example given in Griffith about bananas and oranges would be just as valid (ie. not constituting a formal vector) because they do not reference any spacial coordinate system.
  

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• a tensor of rank 1
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• [perhaps most rigorous...] A vector is a member of a vector space.
  • elements of a vector space obey certain laws:
    they can be added to each other, or multiplied by a scalar, to create another vector.

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eof