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.
Examplesopen allclose all
An approximate MachinePrecision matrix:
Adjust the option Tolerance so that the linear dependence of the eigenvectors is detected:
If a matrix is diagonalizable, it can be decomposed as , where is nonsingular and is diagonal. This can be used to compute a matrix function by using its power series represention as . Use this method to compute several different matrix functions:
Compute MatrixExp of m:
Compute matrix Cosh[x] function of m:
Properties & Relations (7)
The decomposition is given by Eigensystem:
Wolfram Research (2014), DiagonalizableMatrixQ, Wolfram Language function, https://reference.wolfram.com/language/ref/DiagonalizableMatrixQ.html.
Wolfram Language. 2014. "DiagonalizableMatrixQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiagonalizableMatrixQ.html.
Wolfram Language. (2014). DiagonalizableMatrixQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiagonalizableMatrixQ.html