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Question about random vectors?
I don't see the point of joint random vectors. For example, say you have two joint vectors X and Y, where X has n samples and Y has m sanmples. Wouldn't this be equivalent to saying that W has n+m elements (has all of the samples of X and Y put into one vector) Any insight would help.
2 Answers
- Anonymous1 decade agoFavorite Answer
You cannot simply combine two vectors into one vector lik ethis. A vector is not jsut an arbitrary collection of numbered, its specifically a collection of numbers that do not change their relative value no matter how the coordinate system they are defined on is shifted, rotated, or expanded/contracted. In an intuitive sense, this means u can think of them as a direction and a magnitude, in a space of n dimensions, where n is the amount of numbers the vector is defined by.
If you have 2 vectors and take their 'average' ,say, and especially if they are not in the same 'dimension', then you might wind up with a unique vector, but you cannot work backwards. You cannot take a vector and figure out what vectors made it in the first place. So no, these would be 2 completely different things.
- Anonymous1 decade ago
two vectors are dependent if the matrix of their vectors has a zero determinant