How to calculate matrix

Matrix calculation, first confirm whether the matrix can be multiplied. Only when the number of columns in the first matrix is equal to the number of rows in the second matrix can the two matrices be multiplied.

Multiplication between matrices can only be carried out when the number of columns of matrix B is equal to the number of rows of matrix A. The calculation between matrices can be divided into the calculation of matrix and multiple vectors, and then the results are merged, and the returned result is a matrix with the number of columns equal to matrix B and the number of rows equal to matrix A. ..

Mathematically, a matrix refers to a group of complex numbers or real numbers arranged in a rectangular array. It was first put forward by British mathematician Kelly in19th century. It is a common tool in advanced algebra, and its operation is an important problem in the field of numerical analysis. Decomposition of a matrix into a combination of simple matrices can simplify the operation of the matrix in theory and practical application.

Introduction to matrix definition:

1, complex matrix: the elements in the matrix can be real numbers or complex numbers. If all the elements in a matrix are complex numbers, then the matrix is called a complex matrix.

2. Matrix addition: For two matrices A and B with the same size, their sum is defined as a new matrix C, where C[i, j]=A[i, j]+B[i, j].

3. Multiplication of matrices: For two matrices A and B, their product is defined as a new matrix C, where C[i, j]=∑(A[i, k]*B[k, j]), where the value of k ranges from 1 to the number of columns in A or the number of rows in B. ..

4. Matrix transposition: for a matrix A, its transposition is defined as a new matrix B, where B[i, j]=A[j, i]. In other words, the number of rows of B is equal to the number of columns of A, and the number of columns of B is equal to the number of rows of A. ..