Find the minimal polynomial of a matrix:

The corresponding matrix polynomial is zero:

Minimal polynomial of a numeric matrix:

Minimal polynomial of a complex matrix:

Minimal polynomial of a symbolic matrix:

Minimal polynomial of a sparse matrix:

Minimal polynomial of a structured matrix:

Use the minimal polynomial to compute the DrazinInverse:

The coefficients can be used to compute the Drazin inverse:

Verify some properties of the Drazin inverse:

Compare with the result of DrazinInverse:

A random integer square matrix of dimension 3:

A matrix minimal polynomial is often the same as the characteristic polynomial up to a constant factor:

The degree of a matrix minimal polynomial can be strictly lower than the matrix dimension:

The minimal polynomial divides the characteristic polynomial with a polynomial quotient:

Compute a minimal polynomial:

The minimal polynomial of a matrix annihilates the matrix:

Compute a minimal polynomial:

The last element in the diagonal of the Smith normal form of a characteristic matrix gives the minimal polynomial:

Find the last block in the Frobenius normal form:

Extract the last column:

This gives the negatives of the minimal polynomial coefficients with lead coefficient implicitly set to 1: