Matrices

A matrix \(A\) is a rectangular arrangement of numbers in some number field \(\mathbb{F}\). When we say \(A \in \mathbb{F}^{n\times m}\) it means \(A\) has \(n\) rows and \(m\) columns.

Matrices represent linear maps and are also used to represent data, with the common convention that each row contains a sample and each column represents all features measured for all samples.

Matrices can be scaled by an element of its underlying field, and matrices of the same dimension (i.e. with same \(m\),\(n\)) can be added. The most common operation on matrices however is multiplication.

See the Matrix World illustration for an overview on different types of matrices - the book in the main repo, The Art of Linear Algebra is also a great resource.