Working with vectors and matrices

This section gives an introduction to vectors and matrices, and using these to perform mathematical manipulations in Python.

Working with vectors and matrices is common in computational chemistry, as well as in a number of data science and machine learning teachniques that are used to work with large datasets or for chemical informatics. To understand the algorithims behind these various techniques, and how these are implemented in code, it is important to understand the underlying mathematical concepts. Working with vectors and matrices falls within the branch of mathematics called linear algebra. This section will give you an overview of some of the mathematical properties of vectors and matrices, and why using these can be useful when solving particular chemical problems computationally.

Further watching and reading

Although it is not necessary to understand the material in this section, if you are interested in a deeper introduction to vectors, matrics, and linear algebra, we recommend the Essence of Linear Algebra YouTube series by 3Blue1Brown.

Another helpful resource that presents these concepts in a similar way is the Land on Vector Spaces series of Jupyter notebooks from Lorena Barba’s group, which provides Jupyter-friendly tools for visualising vectors and matrix operations.

If you want a more formal textbook, you might want to look at Introduction to Linear Algebra by Gilbert Strang, or the associated lecture videos.