How to calculate the max norm of a vector using Python?

by | Oct 3, 2023 | Linear Algebra

Max Norm Of Vectors

What is the max norm of a vector?

The norm of a vector v is mathematically defined as follows:

L^q=||\vec{v}||_q=(\sum_{k}{|v_k|^q})^{\frac{1}{q}}

When q=1, the vector norm is called the L1 norm or the Manhattan norm. So, the L1 norm of a vector is mathematically defined as follows:

L^1=||\vec{v}||_1=(\sum_{k}{|v_k|})

And when q=2, the vector norm is called the L2 norm or the Euclidean norm. So, the L2 norm of a vector is mathematically defined as follows:

L^2=||\vec{v}||_2=(\sum_{k}{|v_k|^2})^{\frac{1}{2}}

The max norm of a vector is defined as follows:

L^{\infty}=||\vec{v}||_{\infty}=\max_{k}|v_k|

In other words, if we take the absolute values of all the elements of a vector, then the max norm of the vector is the element the absolute value of which is the maximum.

Let’s look at an example. Let’s say v is a vector as given below:

\vec{v}=\begin{bmatrix} 1 \\ 2 \\ -3 \end{bmatrix}

The max norm of the vector v will be:

||\vec{v}||_{\infty}=\max_{k}|v_k|=3

How to calculate the max norm of a vector using Python?

We can use the following Python code to calculate the max norm of a vector using NumPy…

Pages: 1 2
Facebooktwitterredditpinterestlinkedinmail

Related posts:

L2-normHow to calculate the L2 norm of a vector using Python? L1-normHow to calculate the L1 norm of a vector using Python? Normalization Using SklearnNormalization using sklearn Create Row Vectors And Column VectorsHow to create a row vector and a column vector using Python NumPy? One-Sample Z-Test In PythonOne-sample Z-test using Python Matrix-Vector MultiplicationHow to multiply a matrix and a vector using Python NumPy? Vigenere Cipher using PythonImplementing the Vigenere Cipher using Python Calculate Transpose Of A VectorHow to calculate the transpose of a vector using Python NumPy? Vector Addition And SubtractionHow to perform vector addition and subtraction using Python NumPy? Vector Dot ProductsHow to calculate vector dot products using Python NumPy? Plot Gaussian DistributionHow to plot Gaussian distribution using Python? Affine Cipher using PythonAffine Cipher using Python Vector Unit Length Scaling Using SklearnVector Unit Length Scaling using sklearn Vector-Scalar MultiplicationPerform vector and scalar multiplication using Python NumPy Unit VectorWhat is a unit vector? Calculate Quartiles And IQR In PythonHow to calculate quartiles and Inter Quartile Range (IQR) in Python?

Calculate the pseudoinverse of a matrix using Python

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

What is the pseudoinverse of a matrix? We know that if A is a square matrix with full rank, then A-1 is said to be the inverse of A if the following condition holds: $latex AA^{-1}=A^{-1}A=I $ The pseudoinverse or the Moore-Penrose inverse of a matrix is a...
Read More

Cholesky decomposition using Python

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

What is Cholesky decomposition? A square matrix A is said to have Cholesky decomposition if it can be written as a product of a lower triangular matrix and its conjugate transpose. $latex A=LL^{*} $ If all the entries of A are real numbers, then the conjugate...
Read More

Tensor Hadamard Product using Python

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

In one of our previous articles, we already discussed what the Hadamard product in linear algebra is. We discussed that if A and B are two matrices of size mxn, then the Hadamard product of A and B is another mxn matrix C such that: $latex H_{i,j}=A_{i,j} \times...
Read More

Perform tensor addition and subtraction using Python

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

We can use numpy nd-array to create a tensor in Python. We can use the following Python code to perform tensor addition and subtraction. import numpy A = numpy.random.randint(low=1, high=10, size=(3, 3, 3)) B = numpy.random.randint(low=1, high=10, size=(3, 3, 3)) C =...
Read More

How to create a tensor using Python?

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

What is a tensor? A tensor is a generalization of vectors and matrices. It is easily understood as a multidimensional array. For example, in machine learning, we can organize data in an m-way array and refer it as a data tensor. Data related to images, sounds, movies,...
Read More

How to combine NumPy arrays using horizontal stack?

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

We can use the hstack() function from the numpy module to combine two or more NumPy arrays horizontally. For example, we can use the following Python code to combine three NumPy arrays horizontally. import numpy A = numpy.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) B =...
Read More

How to combine NumPy arrays using vertical stack?

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

Let’s say we have two or more NumPy arrays. We can combine these NumPy arrays vertically using the vstack() function from the numpy module. For example, we can use the following Python code to combine three NumPy arrays vertically. import numpy A = numpy.array([[1, 2,...
Read More

Singular Value Decomposition (SVD) using Python

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

What is Singular Value Decomposition (SVD)? Let A be an mxn rectangular matrix. Using Singular Value Decomposition (SVD), we can decompose the matrix A in the following way: $latex A_{m \times n}=U_{m \times m}S_{m \times n}V_{n \times n}^T $ Here, U is an mxm matrix....
Read More

Eigen decomposition of a square matrix using Python

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

Let A be a square matrix. Let’s say A has k eigenvalues λ1, λ2, ... λk. And the corresponding eigenvectors are X1, X2, ... Xk. $latex X_1=\begin{bmatrix} x_{11} \\ x_{21} \\ x_{31} \\ ... \\ x_{k1} \end{bmatrix} \\ X_2=\begin{bmatrix} x_{12} \\ x_{22} \\ x_{32} \\ ......
Read More

How to calculate eigenvalues and eigenvectors using Python?

by | October 3, 2023 | Featured, Linear Algebra | 0 Comments

In our previous article, we discussed what eigen values and eigenvectors of a square matrix are and how we can calculate the eigenvalues and eigenvectors of a square matrix mathematically. We discussed that if A is a square matrix, then $latex (A- \lambda I) \vec{u}=0...
Read More

Amrita Mitra

Author

Ms. Amrita Mitra is an author, who has authored the books “Cryptography And Public Key Infrastructure“, “Web Application Vulnerabilities And Prevention“, “A Guide To Cyber Security” and “Phishing: Detection, Analysis And Prevention“. She is also the founder of Asigosec Technologies, the company that owns The Security Buddy.

0 Comments

Submit a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Not a premium member yet?

Please follow the link below to buy The Security Buddy Premium Membership.

Buy Premium Membership

Featured Posts

Translate »