# Frobenius covariant

## From Wikipedia, the free encyclopedia

In matrix theory, the **Frobenius covariants** of a square matrix A are special polynomials of it, namely projection matrices *A*_{i} associated with the eigenvalues and eigenvectors of A.[1]^{: pp.403, 437–8 } They are named after the mathematician Ferdinand Frobenius.

Each covariant is a projection on the eigenspace associated with the eigenvalue *λ*_{i}.
Frobenius covariants are the coefficients of Sylvester's formula, which expresses a function of a matrix *f*(*A*) as a matrix polynomial, namely a linear combination
of that function's values on the eigenvalues of A.