Diagonal Matrix
A diagonal matrix is a special type of square matrix where all the elements outside the main diagonal are zero. The main diagonal runs from the top left to the bottom right of the matrix. For example, in a 3x3 diagonal matrix, the elements at positions (1,1), (2,2), and (3,3) can have any value, while all other positions contain zeros.
Diagonal matrices are important in linear algebra because they simplify many calculations, such as finding eigenvalues and eigenvectors. They are also used in various applications, including computer graphics and systems of linear equations, making them a fundamental concept in mathematics and engineering.