How to calculate vector dot products using Python NumPy?

by | Oct 3, 2023 | Linear Algebra

Vector Dot Products

What is a vector dot product and how to calculate it?

Let’s say a and b are two n-dimensional vectors. If we perform a dot product or scalar product of a and b, the corresponding elements of the two vectors get multiplied and then, the resultant terms are added to get a single number.

\overrightarrow{a} \cdot \overrightarrow{b}=\sum_{i=1}^{n}a_i b_i

Let’s look at an example. Let’s say a and b are two 3 dimensional row vectors.

\overrightarrow{a} = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \\ \overrightarrow{b} = \begin{bmatrix} 4 & 5 & 6 \end{bmatrix} \\ \overrightarrow{a} \cdot \overrightarrow{b}=\begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 4 & 5 & 6 \end{bmatrix} \\ =\sum_{i=1}^{3}a_i b_i \\ =1 \times 4+2 \times 5 + 3 \times 6 \\ =4+10+18=32

Similarly, we can take two column vectors of the same dimension and perform a dot products of the vectors.

\overrightarrow{c} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \\ \overrightarrow{d} = \begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix} \\ \overrightarrow{c} \cdot \overrightarrow{d}=\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \cdot \begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix} \\ =\sum_{i=1}^{3}c_i d_i \\ =1 \times 4+2 \times 5 + 3 \times 6 \\ =4+10+18=32

…

Pages: 1 2
Facebooktwitterredditpinterestlinkedinmail

Related posts:

Create Row Vectors And Column VectorsHow to create a row vector and a column vector using Python NumPy? Vector Addition And SubtractionHow to perform vector addition and subtraction using Python NumPy? Pandas Select Rows And ColumnsHow to select rows and columns of a DataFrame using loc and iloc in pandas? Calculate Transpose Of A VectorHow to calculate the transpose of a vector using Python NumPy? Pandas Percentage Of Missing DataHow to find the percentage of missing values in a DataFrame using pandas? Vector-Scalar MultiplicationPerform vector and scalar multiplication using Python NumPy NumPy Array With Random NumbersHow to create a NumPy array filled with random numbers? Create NumPy Arrays Using linspaceHow to create a NumPy array using linspace in Python? Pandas Drop Missing ValuesHow to drop missing values from a DataFrame using the pandas Python library? Pandas Find Missing ValuesHow to find the total number of missing values in a DataFrame using the pandas Python library? Pandas loc And ilocHow to select rows of a DataFrame using loc and iloc in pandas? Pandas Concatenate DataFramesHow to concatenate two pandas DataFrames using Python? Create Zero Vectors Using NumPyHow to create a zero vector using Python NumPy? Pandas loc vs. ilocloc vs. iloc in the Pandas Python library Pandas Drop Rows And ColumnsHow to delete a row or column of a DataFrame using Python pandas? NumPy Array ShapeHow to print the shape of a NumPy array?

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 »