Question

The sum of eigenvalues of a matrix is the ______ of the elements of the principal diagonal.

Answer 1

The trace of a matrix is the sum of the elements of the principal diagonal of the matrix. Fact - The sum of Eigen values of a matrix is equal to it's trace. Fact - The product of Eigen values of a matrix is equal to its determinant value.

Answer 2

Answer:

The sum of eigenvalues of a matrix is the __Sum____ of the elements of the principal diagonal

Step-by-step explanation:

• Eigen values are the roots of the characterstic equation.
• The characterstic equation is formed by determinant of matrix

        A-λI=0  , where A is the matrix and I is the identity matrix.

• The sum of the Eigen Values is equal to the trace of the matrix.
• Trace is the sum of the Principal Diagonol Elements.