Vectors vs. matrices

Introduction

core.matrix supports both vectors (1D arrays) and matrices (2D arrays). This page explains the differences between the two.

Matrix properties

• Can be thought of as a 2D nested array, e.g. \[\[1 2 3\] \[4 5 6\] \[7 8 9\]\]
• Always have dimensionality 2; equivalent to a 2D array
• Are indexed by [row column]
• Can be transposed, which reverses rows and columns
• Support some matrix-only operations, e.g. det, trace
• A slice of a Matrix is a 1D vector

Vector properties

• Can be though of as a 1D array, e.g. [1 2 3]
• Always have dimensionality 1; equivalent to a 1D array
• Are indexed by [position]
• Transposing a vector is the identity function: if you call transpose on a vector, you will get the same vector back unchanged
• Supports some vector-only operations, e.g. distance, dot-product
• A slice of a vector is a 0D scalar

Why have both?

Technically, you can always emulate vectors by using matrices. Use either a Nx1 column matrix or a 1xN row matrix. Indeed, some mathematics systems (like MATLAB) expect you to do just this.

However, there are some important reasons that we need to have both:

• core.matrix is designed to be a general purpose N-Dimensional API, so it needs to support both the 1D and 2D cases in general.
• Many underlying matrix implementations have both vectors and matrices. We need to support them.
• It can catch some runtime type errors (e.g. passing a matrix where a vector is required).
• In some cases, using vectors rather than matrices offers higher performance (due to a simpler data structure and less complex indexing).

Which should I use?

Usually this will be clear from what is needed for your problem. If you need a 2D array of numbers then use a matrix. If you need a 1D array of numbers then use a vector.

Further discussion / reading:

• https://groups.google.com/d/topic/numerical-clojure/zebBCa68eTw/discussion