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> You represent a vector by giving two pieces of data, (1) an ordered list of coordinates, and (2) a basis. Ok, I understand. But as used in computer languages
by nyc111 8y ago
> You represent a vector by giving two pieces of data, (1) an ordered list of coordinates, and (2) a basis.
Ok, I understand. But as used in computer languages, a vector can be simply 2 numbers. No coordinates or basis are implied. That's what I meant.
- earthicus 8y agoAha, yes. Computer languages borrowed the word 'vector', but they have basically nothing to do with the mathematical structure from linear algebra. It's best to keep them completely separate in your mind.
- nyc111 8y agoSo in math, when we say "vector" coordinate system is a given, as you explained?
- earthicus 8y agoIf a coordinates are given, then they will be given with respect to a basis. However, it's entirely possible to do things more abstractly without introducing coordinates and bases to begin with, for example: https://en.wikipedia.org/wiki/Tensor_(intrinsic_definition) https://en.wikipedia.org/wiki/Tensor_(intrinsic_definition)