Dalam matematik , ruang Hilbert (dinamakan sempena David Hilbert ) membenarkan pengitlak kaedah algebra dan kalkulus linear daripada ruang Euclidean dua dimensi dan tiga dimensi kepada ruang yang mungkin mempunyai dimensi tak terhingga. Ruang Hilbert ialah ruang vektor dilengkapi dengan operasi produk dalaman, yang membolehkan mentakrifkan fungsi jarak dan keserenjang (dikenali sebagai ortogonal dalam konteks ini). Tambahan pula, ruang Hilbert adalah lengkap untuk jarak ini, yang bermaksud terdapat had yang mencukupi dalam ruang untuk membolehkan teknik kalkulus digunakan.
Keadaan rentetan bergetar boleh dimodelkan sebagai titik dalam ruang Hilbert. Penguraian rentetan bergetar menjadi getarannya dalam nada yang berbeza diberikan oleh unjuran titik ke paksi koordinat dalam ruang.
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