A method for calculating the sum of diagonal and anti diagonal of power matrices without explicitly calculating its matrices

Abstract In fact, matrix power can be done simply by explicitly calculating it using the rule of matrix multiplication. However, matrix power is time consuming if it had high power, because the multiplication is done by many times. Fixing this, the function develops how to calculate the sum of diagonal and anti diagonal of power matrix without explicitly calculating the matrix. The result show that those can be calculated by using linear combination of determinant, sum of diagonal, and sum of anti diagonal of the initial matrix. Beside that, the functions are applied to certain block matrices.