Likewise, if the kets are known, but a set of [[eigenvalues]] of the form:
<math>S=\left\lbrace\lambda_1,\lambda_2,\ldots,\lambda_n,\ldots,\right\rbrace</math>
is also known, then a linear operator possessing those eigenvalues can be constructed. The matrix representation for a linear operator <math>Q</math> with eigenvalues from <math>S</math>: