DiagonalizableMatrixQ

DiagonalizableMatrixQ[m]
gives True if m is diagonalizable, and False otherwise.

Details and OptionsDetails and Options

  • A matrix m is diagonalizable if it is similar to a diagonal matrix. That is, if there is a nonsingular matrix such that is diagonal.
  • DiagonalizableMatrixQ works for symbolic as well as numerical matrices.
  • For approximate matrices, the option Tolerance->t can be used to indicate that the determinant of eigenvectors v of the matrix m satisfying Abs[Det[v]]t is taken to be zero, which means that the eigenvectors v are linearly dependent and the matrix m is not diagonalizable.
  • The option Tolerance has Automatic as its default value.
Introduced in 2014
(10.0)