# Difference between parentheses and angle brackets in vector notation

In my calculus class we used angle brackets to describe vectors, $\langle a, b, c\rangle$. But in my linear algebra class we use parenthesis. I've read here the angle brackets are for inner products but in calc we've used them generally, not necessarily when computing a product; we've said u $= \langle a,b,c\rangle$. When are parentheses or angle brackets used properly?

• Just like some people spell "color" as "colour" some people write $(a,b,c)$ as $\langle a,b,c \rangle$. There is no difference beyond personal preference. Commented Mar 13, 2014 at 3:55
• Sometimes the inner product of vectors $\mathbf u$ and $\mathbf v$ is written as $\langle \mathbf u,\mathbf v\rangle$. If your vectors are written as $\langle a,b,c\rangle$ and $\langle x,y,z\rangle$, then the inner product might be written as $\langle a,b,c\rangle\cdot\langle x,y,z\rangle$. The meaning of the angle brackets should be clear from the context. Commented Mar 13, 2014 at 4:01
• The vector police will be by to see you shortly. Using angle brackets like that is a gateway notational abuse and will lead to writing open intervals as $]0,1[$ and the like. Commented Mar 13, 2014 at 5:35
• @copper.hat: Isn't that the proper way to write open intervals?
– Zaz
Commented Jul 4, 2015 at 1:45
• @Zaz: My comment was meant in a light hearted way. Some folks use $]0,1[$ to indicate an open interval to avoid confusion with other notations (inner product, pairs, etc.). However, in practice there is rarely a confusion. Commented Jul 4, 2015 at 9:47

Given that a vector is minimally described by its magnitude and direction and is NOT necessarily fixed in space, the way I see it is that $$\langle a, b, c\rangle$$ is one way (a very common way) to describe the vector and is interpreted thus: "if you started at the origin, then the vector would terminate at point (a, b, c). So...
$$\langle a, b, c\rangle$$ describes any vector that is equivalent to the specific vector starting at (0, 0, 0) and terminating at (a, b, c)