INNER PRODUCT ON VECTOR SPACES OVER A FINITE FIELD
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 posi...
Saved in:
| Main Author: | |
|---|---|
| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/81549 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
|---|