For 10 points, identify these numbers associated with a given square matrix, which are the coefficient of proportionality when a matrix is applied to an eigenvector
Vieta's formula can be used to show that the sum of these quantities always equals the trace. One consequence of the spectral theorem is that a change of coordinates can be applied so that these entities all lie along the diagonal. All of these numbers equal one for a rotation, since vector lengths remain unchanged. These are the numbers lambda so that A minus lambda times the identity matrix is singular, which makes these entities the roots of the characteristic polynomial. For 10 points, identify these numbers associated with a given square matrix, which are the coefficient of proportionality when a matrix is applied to an eigenvector
Vieta's formula can be used to show that the sum of these quantities always equals the trace.
eigenvalues [prompt on "lambda" until mentioned]