What is matrix division?

In mathematics, matrix division refers to the process of dividing one matrix by another. However, unlike scalar division, matrix division is not always well defined. Matrix division is only possible if the two matrices involved meet certain criteria, such as being square and invertible.

There are different methods for computing matrix division, including finding the inverse of the second matrix and multiplying it with the first matrix, or solving a system of linear equations. It is important to note that matrix division is not commutative, meaning that AB ≠ BA in general, where A and B are both matrices.

Matrix division is commonly used in applications involving linear algebra, such as in solving systems of equations, optimization problems, and signal processing. It is also used extensively in machine learning, where matrices are used to represent data and perform various operations on it.