Open AccessA method for calculating the sum of diagonal and anti diagonal of power matrices without explicitly calculating its matrices
Author(s) -
Amihood Amir,
G. Jeriko,
M. Jusmawati
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1277/1/012038
Subject(s) - diagonal , diagonal matrix , main diagonal , block matrix , mathematics , matrix (chemical analysis) , multiplication (music) , band matrix , matrix multiplication , power (physics) , function (biology) , square matrix , symmetric matrix , combinatorics , physics , geometry , eigenvalues and eigenvectors , materials science , quantum mechanics , evolutionary biology , composite material , quantum , biology
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.