TITLE: How to find the absolute value of a vector?
QUESTION [13 upvotes]: In my linear algebra course I keep seeing something like this:
a = {1, 3, 5}
Then in formulas I see this:
|a|
What does this mean, what is the absolute value of a vector? Wouldn't just be {1,3,5}?

REPLY [10 votes]: Absolute value of a vector means taking second norm of the vector i.e. $\|x\|$. That means the same thing as $\sqrt{x_1^2 +x_2^2+...+x_n^2}$. I don't understand why some top researchers in computer science abuse the notation where $|x|$ is widely used for absolute value of scalars in math.
I have also seen papers using $|x|$ to mean absolute value of each component of the vector $x$. In summary, meaning will depends upon the context and author.