Matrix notation differences So I'm in an elementary matrix and linear algebra class and during lecture my professor uses this notation for a matrix: $$\left(\begin{matrix}a & b\\c&d\end{matrix}\right)$$ but in my textbook it uses $$\left[\begin{matrix}a & b\\c&d\end{matrix}\right]$$ Is there a difference here? 
 A: $$\left(\begin{matrix}a & b\\c&d\end{matrix}\right)\quad = \quad \left[\begin{matrix}a & b\\c&d\end{matrix}\right]$$ 
"Is there a difference here?" Not at all. 
Just search this site for "matrices" and you'll see both the use of parentheses and brackets, with similar frequency.
Similarly, with vectors, you'll see them written as ordered 'tuples with parentheses and sometimes in brackets:
$(\vec{v_1},...,\vec{v_n}) = [\vec{v_1},...,\vec{v_n}]\quad$ and $\quad (\vec{v_1},...,\vec{v_n})^T = [\vec{v_1},...,\vec{v_n}]^T$

It is probably easier on a chalkboard (or by hand, for that matter) to write matrices with parentheses, whereas in typesetting, one way is as easy as the other.
A: The body must be at least 30 characters, but the answer needs only three:
No.
A: There's no difference there. By the way, my understanding is that in Russia, it is common to denote a matrix by
$$\begin{vmatrix}
a& b\\ c &d
\end{vmatrix}$$
and its determinant by
$$\begin{Vmatrix}
a& b\\ c &d
\end{Vmatrix}$$
whereas (at least in the US) we would use the first of these notations for the determinant, and one of the notations you mention in your question for the matrix itself.
Edit: I've had two Russian professors who I've seen use single bars for their matrices (and no one else ever did), and I seemed to remember this notation was used in Shilov's Linear Algebra, an older textbook from Russia, which is what led me to answer as I did. However, I checked in Shilov, and it appears he uses double bars for matrices, and single bars for the determinant:




