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Gram-Schmidt 正交化(英文:Gram–Schmidt process)係喺一個內積空間入面,由一柞向量獲得一組正交向量嘅方法,喺線性代數同數值分析入面都好有用。好多時呢個內積空間係講緊歐幾里得空間配以標準內積(即係點積)。如果原本畀嗰柞向量係一組基嘅話,出嚟嘅結果就會係一組正交基。
畀一個矩陣,如果佢嘅直行係滿階嘅話,對佢嘅直行做 Gram-Schmidt 正交化就會得到個矩陣嘅 QR 分解(將矩陣分解成正交矩陣同三角矩陣乘埋)。
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