1. Matrix addition and subtraction: Two identical matrices can be added or subtracted. Addition requires the same number of rows and columns in the two matrices, while subtraction requires the same number of rows and columns in the first and second matrices.
2. Matrix multiplication: two matrices are multiplied to get a new matrix. Multiplication requires that the number of columns in the first matrix is equal to the number of rows in the second matrix.
3. Matrix transposition: Matrix transposition is a new matrix obtained by exchanging the positions of rows and columns of the matrix.
4. identity matrix: identity matrix is a square with 1 on its main diagonal, and all other elements are 0. Identity matrix times any matrix equals the original matrix.
5. Zero matrix: A zero matrix is a square matrix with all elements of 0. A zero matrix multiplied by any matrix equals a zero matrix.
6. Inverse matrix: If a square matrix A is multiplied by its inverse matrix B to get identity matrix I, then A is called invertible matrix, and B is the inverse matrix of A ... Only a full rank square matrix has an inverse matrix.
7. Determinant: The determinant of the n-order square matrix is a special numerical value, which can indicate the degree to which the linear transformation represented by the square matrix "stretches" the space.