Diagonal Matrices

Diagonal Matrices

A diagonal matrix is a square matrix with zeros off the principal diagonal and the elements on the principal diagonal may or may not be non-zero.

or

where is a scalar and is the Kronecker delta.

Properties of Diagonal Matrix

Multiplication of two diagonal matrices A and B are commutative

If only B is a diagonal matrix, in general, the matrix products are not commutative.

Power of Diagonal Matrix

Elements of the power of a diagonal matrix, equals to the power corresponding elements of the orginal matrix , where k is a positive integer.

Inverse of Diagonal Matrix

The inverse of a diagonal matrix with all non-zero principal diagonal elements is also a diagonal matrix. The principle diagonal elements of the inverse equal to the reciprocals of the corresponding elements of the orginal matrix.

Since , imply