# Is the “dimension” in dimensional analysis the same as the “dimension” in “three spatial dimensions”?

When we talk about the dimension of a quantity (e.g. the dimension of acceleration is$[ L \ T ^ {-2}]$) are we talking about the same "dimension" as when we talk about three dimensional space?

Are these two separate definitions sharing a word? or are they two uses of the same meaning?

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The dimension of a space is the dimensional analysis dimension of volumes, when a unit of length is given. –  Ron Maimon May 16 '12 at 5:53

The most straightforward, nontechnical explanation is that these are two different meanings for the same word.

However, you can actually think of the units of a quantity as an element in a vector space, whose dimensions are labeled $M$, $L$, $T$, etc., and you can also think of regular three dimensional space as a vector space, whose dimensions are labeled $x$, $y$, and $z$. With this, it's still not quite the same meaning of "dimension," since you might say $L T^{-2}$ is a dimension but you wouldn't say $y - 2z$ is a dimension; however, that does help motivate why the same word is used for both concepts.

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Thank you for your answer! I think that "vector space" was what I needed to hear. –  MatrixManAtYrService May 16 '12 at 17:17