# 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. 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. 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. Mar 13, 2014 at 5:35
• @copper.hat: Isn't that the proper way to write open intervals?
– Zaz
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. 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...

(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... Jun 5, 2019 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. Jun 5, 2019 at 23:35
• Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, use MathJax. Jun 5, 2019 at 23:35