Matrix calculation is an important content in linear algebra, involving matrix addition, subtraction, multiplication, transposition, inversion and other operations. The definitions and properties of these matrix calculation operations will be introduced one by one.
1, matrix addition
Matrix addition refers to adding two matrices with the same dimension.
Matrix a and matrix b must have the same number of rows and columns. Every element C[i][j] of matrix c is equal to the sum of matrix A[i][j] plus matrix B[i][j].
2. Matrix subtraction
Matrix subtraction refers to subtracting another matrix with the same dimension from one matrix.
Matrix a and matrix b must have the same number of rows and columns. Every element C[i][j] of matrix c is equal to the difference between matrix A[i][j] and matrix B[i][j].
3. Matrix multiplication
Matrix multiplication refers to multiplying two matrices to get a new matrix.
The number of columns of matrix A must be equal to the number of rows of matrix B. The number of rows of matrix C is equal to that of matrix A, and the number of columns is equal to that of matrix B. Each element C[i][j] in matrix C is equal to the sum of the products of the I-th row element of matrix A and the J-th column element of matrix B.
4, transpose matrix
Transposition matrix refers to a new matrix obtained by exchanging the positions of rows and columns of a matrix.
The number of rows of matrix A is equal to the number of columns of matrix B, and the number of columns is equal to the number of rows of matrix B. Each element B[i][j] of matrix B is equal to matrix A[j][i], that is, the element in row I and column J of B is equal to the element in row J and column I of A.
5, matrix inversion
Matrix inversion refers to finding the inverse matrix of a matrix so that the product of two matrices is equal to identity matrix.
Matrix a must be a square (the number of rows equals the number of columns). Matrix B is the inverse of matrix A, if and only if matrix A is multiplied by matrix B, and matrix B multiplied by matrix A equals identity matrix.
These matrix calculation formulas are the basic concepts in linear algebra, from which more complex and advanced matrix calculation rules and formulas can be derived. They are widely used in mathematics, engineering, computer science and other fields.