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. – Brian Fitzpatrick Mar 13 '14 at 3:55
• How about when computing an inner product? Is that when angle brackets are used exclusively? – Al Jebr Mar 13 '14 at 3:56
• 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. – Brian Fitzpatrick Mar 13 '14 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. – copper.hat Mar 13 '14 at 5:35
• @copper.hat: Isn't that the proper way to write open intervals? – Zaz Jul 4 '15 at 1:45

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...

(a, b, c) is an exact point in the xyz coordinate space

$$\langle a, b, c\rangle$$ describes any vector that is equivalent to the specific vector starting at (0, 0, 0) and terminating at (a, b, c)

Here is an MIT problem set that uses both to describe the same parallelogram • (1) Please do not delete an answer, then repost a new answer which is essentially the same. This is poor etiquette, and is considered by some to be something of an abuse of the site. (2) What do you mean by "equivalent"? Your explanation is still quite imprecise... – Xander Henderson Jun 5 at 23:22
• Thank you for your comments and feedback regarding etiquette here. I wasn't aware that deleting was bad form. I was embarrassed with my original answer. With regards to my revised answer, my understanding is that vectors are equal when they have the same magnitude and the same direction. – triple.vee Jun 5 at 23:35
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