DiagonalizableMatrixQ

DiagonalizableMatrixQ[m]

gives True if m is diagonalizable, and False otherwise.

Details 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.

Examples

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Basic Examples  (1)

Test if a matrix is diagonalizable:

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Scope  (6)

Options  (1)

Applications  (1)

Properties & Relations  (7)

See Also

NormalMatrixQ  HermitianMatrixQ  AntihermitianMatrixQ  PositiveDefiniteMatrixQ  MatrixQ  VectorQ  ArrayQ

Tutorials

Introduced in 2014
(10.0)