If an eigenvalue of a matrix
is known, explain how the reduced row echelon form operation can be used
to find the eigenvectors.
How are the determinant
of a matrix and its eigenvalues related? Describe this carefully -- what
should the rule say if an eigenvalue is repeated? What should it say if
the matrix has a pair of conjugate complex eigenvalues?
Describe the trace of a
matrix in terms of the entries of the matrix.
How are the trace of a
matrix and its eigenvalues related? Describe this carefully -- what should
the rule say if an eigenvalue is repeated? What should it say if the matrix
has a pair of conjugate complex eigenvalues?
