If it is the addition and multiplication of matrices, it is called the linear operation of matrices; If it is the addition and multiplication of vectors, it is collectively called the linear operation of vectors. Different linear operations generally have different forms, which meet the laws of exchange, association and distribution.
Extended data:
The addition of matrix is the addition of corresponding elements of matrix. Of course, the added matrices must have the same number of rows and columns, that is, only the same type of matrices can be added. Since matrix addition comes down to the addition of their elements, that is, the addition of numbers, it is not difficult to verify whether matrix addition is satisfied.
A matrix is decomposed into the sum or product of several relatively simple or characteristic matrices. Matrix decomposition methods generally include triangle decomposition, spectral decomposition, singular value decomposition, full rank decomposition and so on.