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Produced by Charles Wells     Revised 2017-01-19
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Delimiters are pairs of symbols used in the symbolic language either for enclosing expressions or as operators.

"( )"

"[ ]"

"$\mathbf{\langle}$ $\rangle$"

"{ }"

Bare delimiters

The notation $(a,b)$

The notation "$(a,b)$" may denote any of these functions:


Matrices may be enclosed by parentheses; for example: \[\left( \begin{matrix} {{a}_{11}} & {{a}_{12}}& {{a}_{13}}\\ {{a}_{21}} & {{a}_{22}} & {{a}_{23}}\\ {{a}_{31}} & {{a}_{32}} & {{a}_{33}}  \\ \end{matrix} \right)\]

This matrix is one single math object with $9$ parameters. It is not in any sense a set of $9$ numbers. It is one matrix.

Square brackets may be used for this as well, as in  \[\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}}& {{a}_{13}}\\ {{a}_{21}} & {{a}_{22}} & {{a}_{23}}\\ {{a}_{31}} & {{a}_{32}} & {{a}_{33}}  \\ \end{matrix} \right]\]

However, vertical bars, as in \[\left| \begin{matrix} {{a}_{11}} & {{a}_{12}}& {{a}_{13}}\\ {{a}_{21}} & {{a}_{22}} & {{a}_{23}}\\ {{a}_{31}} & {{a}_{32}} & {{a}_{33}}  \\ \end{matrix} \right|\] is by definition the determinant of the matrix, which is a single number. It is not a matrix at all.


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