What does $|\langle A,B \rangle|$ mean?

Question

I was wondering what $|\langle A,B \rangle|$ mean, where both are vectors, if I am correct.

Thanks!

Answer 1

As Timbuc mentions this probably means the absolute value of the inner product of the vectors.

However, the inner product can mean different things in different contexts - the point of an inner product is to associate any two vectors in some space with a scalar in a nice manner (specifically this manner). Without further information, and if you are working with vectors in a Euclidean space, the inner product probably refers to the dot product between the two vectors. As a reminder, if the two vectors are $A=(a_1,a_2,\dots,a_n)$ and $B=(b_1,b_2,\dots,b_n)$, then the dot product is defined as $a_1b_1+a_2b_2+\dots+a_nb_n$, so in this case we would have

$$|\langle A,B\rangle|=|a_1b_1+a_2b_2+\dots+a_nb_n|$$