A sesquilinear form is a modification of a [tag:bilinear-form], where it allows one of its arguments to be "twisted" in a [tag:semilinear] manner.
One of its applications is when taking the inner product of two complex vectors. It guarantees the the result is a real number by twisting the linearity of one of the arguments by taking its complex conjugate and then performing a standard inner product with the other argument.
A sesquilinear form is a modification of a bilinear-form, where it allows one of its arguments to be "twisted" in a semilinear manner.
One of its applications is when taking the inner product of two complex vectors. It guarantees the the result is a real number by twisting the linearity of one of the arguments by taking its complex conjugate and then performing a standard inner product with the other argument.