How to find the multiplicity of an eigenvalue?
If you have a square or hermitian matrix, then the multiplicity of an eigenvalue is the number of linearly independent eigenvectors. If you have an endomorphism, then the multiplicity of an eigenvalue is the corank of the endomorphism at that eigenvalue.
How to find the multiplicity of
To find the multiplicity of an eigenvalue, we need to find the algebraic multiplicity (sometimes called geometric multiplicity) as well as the algebraic multiplicity. The algebraic multiplicity of an eigenvalue is the number of linearly independent eigenvectors associated with that eigenvalue. If the algebraic multiplicity of an eigenvalue is one, then the eigenvalue is simple and has an eigenvector. If the algebraic multiplicity of an
How to find the multiplicity of an eigenvalue in characteristic polynomial?
If you know the characteristic polynomial, you can check the multiplicity of an eigenvalue by solving the system of equation. The system of equation is formed by the coefficients of the characteristic polynomial multiplied by the roots. Here are the steps:
What is the multiplicity of an eigenvalue?
In general, the multiplicity of an eigenvalue is the number of linearly independent eigenvectors associated with the eigenvalue. All the eigenvectors associated with an eigenvalue are linearly independent if and only if the matrix $A$ that you consider is invertible, or equivalently, is square and has full rank; otherwise, the eigenvectors would span a subspace of dimension less than $n$.
How to find multiplicity of an eigenvalue in finite field?
Let $\lambda$ be an eigenvalue of $A$ over the field $GF(q)$. If $|G|$ is the order of the automorphism group of $GF(q)$, then we have $\lambda^{\frac{q-1}{|G|}}=1$. So the eigenvalues of $A$ are of the form $\lambda^{\frac{q-1}{|G|}}$, where $|G|$ is the
