For 10 points, identify this scalar value, usually symbolized by lambda, that indicates that a matrix times some vector x is equal to this integer quantity times the vector x.
These quantities must be real when all of the complex entries equal their conjugate transpose, as is the case in a Hermitian matrix. They can be obtained by solving the determinant of the matrix minus these variables times the identity matrix and solving for zero, a process that yields the characteristic equation of the matrix. For 10 points, identify this scalar value, usually symbolized by lambda, that indicates that a matrix times some vector x is equal to this integer quantity times the vector x.
These quantities must be real when all of the complex entries equal their conjugate transpose, as is the case in a Hermitian matrix.
{Eigenvalues} (or {Characteristic Roots}, {Characteristic Values}, {Proper Values}, or {Latent Roots})