Mathematics — Unit 1 — Test 23

If F is a field and f(x)∈F[x] is irreducible of degree m, then F[x]/(f)

For finite fields, the number of monic irreducible polynomials of degree d over F_q equals

In F_{p^n}, the subfield fixed by σ^k (Frobenius^k) has size

Let V be a finite‑dimensional vector space and T:V→V linear. The polynomial of least degree annihilating T is

If V has dim n and T has rank r, then nullity(T) equals

A linear operator T on C^n is diagonalizable by a unitary matrix iff T is

For a Hermitian matrix H (complex), which statement holds?

If T is nilpotent of index k (T^k=0, T^{k−1}≠0) on an n‑dimensional space, then the minimal polynomial is

Jordan canonical form of a matrix exists over