The sum of the eigenvalues of a matrix is equal to the sum of its diagonal elements, called the trace of a matrix. 2. The product of the eigenvalues of a matrix is equal to the determinant of the matrix. In example (5) above, the trace is 0 = √5+(− √5) and the determinant is −5 = √5 x − √5.
How do you find the eigenvalues of a diagonal matrix?
The eigenvalues of B are 1,4,6 since B is an upper triangular matrix and the eigenvalues of an upper triangular matrix are diagonal entries. We claim that the eigenvalues of A and B are equal.
What are the eigenvalues of a triangular matrix?
The eigenvalues of B are 1,4,6 since B is an upper triangular matrix and the eigenvalues of an upper triangular matrix are diagonal entries. We claim that the eigenvalues of A and B are equal.