Contents
Introduction
The norm function is a mathematical concept that measures the size or length of a mathematical object, such as a vector or a matrix. It is often denoted by enclosing the object in double vertical bars, also known as the norm bars. There are different types of norms, such as the Euclidean norm, the 1-norm, and the infinity norm, among others.
To write the norm function in LaTeX, you can use the following notation:
\left \lVert x \right \rVert
You can also just use \Vert instead of \lVert and \rVert:
\left \Vert x \right \Vert
or you can simply use the double vertical bar symbol:
\left \| x \right \|
all of which render as $\left \lVert x \right \rVert$.
You can define a command for the norm function as follows:
\newcommand{\norm}[1]{\left \lVert #1 \right \rVert}
This command allows you to easily use the norm function in your LaTeX document by typing \norm{x}.
Different Types of Norms
In addition to the general notation for the norm function, you can specify different types of norms by adding a subscript. Here are a few examples:
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Euclidean Norm (2-norm): The Euclidean norm, also known as the 2-norm or the Euclidean length, is commonly used and represents the straight-line distance in Euclidean space. It is denoted as $\left \lVert x \right \rVert_2$.
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1-Norm: The 1-norm, also known as the Manhattan norm or the taxicab norm, calculates the sum of the absolute values of the components. It is denoted as $\left \lVert x \right \rVert_1$.
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Infinity Norm (Max Norm): The infinity norm, also known as the maximum norm or the supremum norm, calculates the maximum absolute value of the components. It is denoted as $\left \lVert x \right \rVert_\infty$.
To write these specific norms in LaTeX, you can add the appropriate subscript e.g. for the Euclidean norm you can write:
\left \lVert x \right \rVert_2
which renders as $\left \lVert x \right \rVert_2$.
You can also create a newcommand using the same approach as before. For example:
\newcommand{\norm}[2]{\left \lVert #1 \right \rVert_{#2}}
This command allows you to write the norm function with a specified subscript e.g. \norm{x}{2} renders as $\left \lVert x \right \rVert_2$.
Conclusion
To summarise, we have learned about the norm function in mathematics and how to write it in LaTeX. We have also learned how to write different types of norms, such as the Euclidean norm, the 1-norm, and the infinity norm, among others.