Matriks Fundamental II

Achmad Arifin (Bagian Matematika ITB)

Journal of Mathematical and Fundamental Sciences
Vol. 6 No. 3 (1972)

Ringkasan. Suatu matriks kwadratis kita katakana fundamental djika ia simetris dan setiap submatriks utamanja mempunjai deretminan jang positif. Misalkan f suatu bentuk bilinier pada suatu ruang vector berdimensi hingga atas lapangan riil, dan f berkoresponensi dengan suatu matriks G. kita buktikan, bahwa f suatu hasilkali-dalam djika dan hanja djika G fundamental.Abstract. We define a square matrix to be fundamental if it is symmetric and all its principal submatrices have positive determinants. Let f be a bilinear form on finite-dimensional vector space over the real field which corresponds to a matrix G. We prove that f is an inner-product if and only if G is fundamental.