Frobenius covariant

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 $A$ .

^ Roger A. Horn and Charles R. Johnson (1991), Topics in Matrix Analysis. Cambridge University Press, ISBN 978-0-521-46713-1

[horn-1] Roger A. Horn and Charles R. Johnson (1991), Topics in Matrix Analysis. Cambridge University Press, ISBN 978-0-521-46713-1

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