The Tree Of Life is almost a matrix – Implications between statements in predicate logic, represented by matrices like this one: File:Predicate logic; 2 variables; 12diag f.svg (Photo credit: Wikipedia)

Paul has a succint online note on vectors and matrices. Vectors are basically a subset of matrices in that they are single row or single column matrices.

Paul’s notes are here.

Matrices are defined as rectangular arrays, which limits matrices to a maximum of two dimensions. There are several types of special matrices subclasses, including (as mentioned above) single dimension matrices or vectors, square matrices (same number of rows and columns), and others.

Paul’s notes also summarizes matrices operations very well. Wikipedia further provides greater breadth and depth to a summary of the subject.

Wikipedia article is here.

Multi-dimensional arrays are called tensors. They have a different set of operations, subclasses and other details although most are extensions of the same concept for matrices.

Wikipedia article on tensors.

Vectors and matrices are used heavily in neural network computations.

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