English Dictionary

normal basis

noun

(algebra, field theory) For a given Galois field 𝔽_(qᵐ) and a suitable element β, a basis that has the form {β, β^q, β^(q2), ... , β^(qm-1)}.

A normal basis is a basis for a vector space over a field in which every element can be expressed uniquely as a linear combination of the basis elements.

意味（1）

(algebra, field theory) For a given Galois field 𝔽_(qᵐ) and a suitable element β, a basis that has the form {β, β^q, β^(q2), ... , β^(qm-1)}.

A normal basis is generated by the repeated action of the Frobenius endomorphism on a suitable element β; it is the orbit of β for that endomorphism.