Abstract: By using the matrix method, the present paper describes all the horomorphisms from the general linear group GL_n(F₂)(n≥3) over the field F₂ with two elements into the general linear group GL_n(K) over a fie ld K. If Ch K≠2, the characterization of the homomorphisms from GL ₃(F₂) into GL₃(K) is given, and it is proved th at the homomorphisms from GL_n(F₂) into GL_n(K) are trivial whenever n≥4； if Ch K≠2 and n≥3 , homomorphisms from GL_n(F₂) into GL_n(K) are ch aracterized.

Key words: field, linear group, involution, homomorphism