Complex sentence: Compare with a bilinear form, which is linear in both arguments; although it should be noted that many authors, especially when working solely in a complex setting, refer to sesquilinear forms as bilinear forms.
Split into simpler sentences: Compare with a bilinear form, which is linear in both arguments. N.B. Many authors, especially when working solely in a complex setting, refer to sesquilinear forms as bilinear forms.