Applied Mechanics Lab

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Engineering Optimization: Notation

Symbol	Definition
$\mathbb{N}$	The set of natural numbers
$(\cdot)$	Denotes an order set
$(x^1,x^2,\ldots, x^n)$ and $(x_1,x_2,\ldots, x_n)$	These symbols denote $n \times 1$ matrices. They are also referred to as $n$-tuples
$\left(x^i\right)_{i=1}^{n}$ and $\left(x_i\right)_{i=1}^{n}$	Short hand for $(x^1,x^2,\ldots, x^n)$ and $(x_1,x_2,\ldots, x_n)$, respectively
$(x^{i;*})$	short for $(x^{1;},x^{2;}\ldots, x^{n;*})$
$(x^i)$ and $(x_i)$	short hand for $(x^i)^{n}_{i=1}$ and $(x_i)^{n}_{i=1}$, respectively
$(A_{ij})_{i,~j=1}^{n}$ and $(A_{ij})$	Denote $n \times n$ square matrices. The index $i$ identifies the row number and $j$ denotes the column number.
$f[\cdot]$	The square parentheses enclose the arguments of the function $f$

[edit]

Symbol	Definition
\(\mathbb{N}\)	The set of natural numbers
\((\cdot)\)	Denotes an order set
\((x^1,x^2,\ldots, x^n)\) and \((x_1,x_2,\ldots, x_n)\)	These symbols denote \(n \times 1\) matrices. They are also referred to as \(n\)-tuples
\(\left(x^i\right)_{i=1}^{n}\) and \(\left(x_i\right)_{i=1}^{n}\)	Short hand for \((x^1,x^2,\ldots, x^n)\) and \((x_1,x_2,\ldots, x_n)\), respectively
\((x^{i;*})\)	short for \((x^{1;},x^{2;}\ldots, x^{n;*})\)
\((x^i)\) and \((x_i)\)	short hand for \((x^i)^{n}_{i=1}\) and \((x_i)^{n}_{i=1}\), respectively
\((A_{ij})_{i,~j=1}^{n}\) and \((A_{ij})\)	Denote $n \times n$ square matrices. The index $i$ identifies the row number and $j$ denotes the column number.
\(f[\cdot]\)	The square parentheses enclose the arguments of the function \(f\)