TY  - JOUR
T1  - Extended Gram-Schmidt process on sesquilinear spaces over finite fields
AU  - Prasetia, Yasin
AU  - Kurnia, Rian
AU  - Andriko, Andriko
AU  - Astuti, Pudji
PY  - 2025
DA  - June
Y2  - 2025
DO  - 10.24330/ieja.1718902
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 1
EP  - 14
LA  - en
AB  - Orthonormal bases play an important role in the geometric study of vector spaces. For inner product spaces over real or complex number fields, we can apply Gram-Schmidt algorithm to construct an orthonormal subset from a linearly independent subset. However, on  sesquilinear spaces over finite fields, Gram-Schmidt algorithm fails to produce an orthonormal subset because of the presence of non-zero, self-orthogonal vectors. In fact, there is a subspace that does not contain an orthonormal basis. In this paper, we study sesquilinear spaces over finite fields and show that a non-zero subspace has an orthonormal basis if and only if it is non-degenerate. An Extended Gram-Schmidt Process (EG-SP) is then discussed  to construct an orthogonal subset from a linearly independent subset having equal generated subspaces. An advantage of the proposed EG-SP is that the obtained orthogonal subset is orthonormal when the generated subspace is non-degenerate.  In addition, we can also extend an orthonormal subset of a sesquilinear space to an orthonormal basis.
KW  - Finite field
KW  - sesquilinear product
KW  - self-orthogonal
KW  - orthonormal subset
KW  - Gram-Schmidt process
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UR  - https://doi.org/10.24330/ieja.1718902
L1  - https://dergipark.org.tr/en/download/article-file/4955827
ER  -