INNER PRODUCT ON VECTOR SPACES OVER A FINITE FIELD - Yulia Widiazhari, Hasna
Inner product is a mapping on a vector space which plays an important role in Mathematics. Inner product is commonly defined on vector spaceS over a real or complex field due to its non-negativity property. On Rn or Cn spaces, inner product can always be associated with the dot product and a positive definite matrix. This final project extends concept of inner products on vector spaces over a finite fields. The research was carried out by observing possible properties of inner product on vector spaceS over a finite field due to properties of real and complex inner products as a reference. As a result, Euclidean inner product on vector spaces over a finite fields has similar properties to real inner product. Furthermore, Hermit inner product on vector spaces over a finite fields has similar properties to complex inner product. Further research show that inner product on Fnq space can be associated to the dot product and a non-singular matrix.