Matrix, in higher mathematics, is often used to describe the relationship between two vectors. In electrical equipment, if it is necessary to establish a switchable connection between multi-input and multi-output, this kind of switching equipment is often named "XXX matrix".
A relatively simple switching matrix is to connect only one output with one input, allowing one input to connect multiple outputs at the same time, but not multiple inputs to connect one output at the same time. Complex switching matrix allows multiple inputs to be connected to one output after weighted superposition.
For example, in a simple switching matrix, output 1= input 1, output 2= input 2, and output 3= output 4= input 3. Here, each output can be independently selected among the inputs, regardless of the situation of other output channels, which can be different from or the same as other outputs. Another example is the switching matrix of 8-out-of-4, which means that there are 4 independent outputs, each of which can be selected from 8 inputs, or there are 4 independent 8-out-of-1. What is often confused with this is the concept of allocation, for example, one out of eight is one out of four, which means that one output is selected from eight inputs and allocated into four identical outputs. Although there are four outputs in appearance, these four outputs are the same, not independent.
Generally, the structure that forms M×N is called a matrix, while the structure that forms M×1 is called a switch or selector, but in fact, it's just N=1, and we treat it as a matrix when discussing it.