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gives the characteristic polynomial for the matrix m.
gives the generalized characteristic polynomial with respect to a.
  • m must be a square matrix.
  • It can contain numeric or symbolic entries.
  • is essentially equivalent to Det where id is the identity matrix of appropriate size. »
Click for copyable input
Click for copyable input
Use exact arithmetic to find the characteristic polynomial:
Use machine arithmetic:
Use 20-digit precision arithmetic:
The characteristic polynomial of a complex matrix:
The generalized characteristic polynomial :
Find the eigenvalues of a matrix as the roots of the characteristic polynomial:
The characteristic polynomial is equivalent to Det:
The generalized characteristic polynomial is equivalent to Det:
A matrix is a root of its characteristic polynomial (Cayley-Hamilton theorem []):
Evaluate the polynomial at m with matrix arithmetic:
Use the more efficient Horner's method to evaluate the polynomial:
where are the eigenvalues is equivalent to the characteristic polynomial:
If is a monic polynomial, then the characteristic polynomial of its companion matrix is:
Form the companion matrix:
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