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When I first learned linear algebra, both the professor and the book used brackets like [ and ] to enclose matrices. However, in my current differential equations textbook, matrices are enclosed by parenthesis, and I suddenly realize everybody else are using them too.

So are brackets/parenthesis for enclosing matrices always totally interchangeable?

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up vote 9 down vote accepted

It is just a question of notation and what you are comfortable with. The only thing you might want to be aware is |A| stands for determinant of the matrix A and hence cannot be used in place of () or [] to represent the matrix

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They're interchangeable. I think a lot of people tend to use parentheses just because they're easier to write by hand.

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@Michale Lugo: and less easy to confuse with vertical bars, which denote determinants (at least to me)... – Arturo Magidin Nov 10 '10 at 5:09
I actually used to hate parentheses for matrices for some reason; it always seemed "less rigorous." Then I had to TA for linear algebra... It is much easier to slap some parentheses on the board than brackets =) – Bey Nov 10 '10 at 6:03
Bey, I'm teaching game theory this semester. Lots of matrices. You bet I'm using parentheses. (And I even use parentheses in things I write up in LaTeX, like solutions to the homework, just for consistency.) – Michael Lugo Nov 10 '10 at 16:02

There are two notations for matrices, ( ), [ ]. Use the one with which you are comfortable with.
Below are examples of both for the 3x3 Identity matrix. $$ \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \\ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} $$

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