基本介紹
- 中文名:基變換
- 外文名:Base conversion
- 性質:幾何技巧
- 套用範圍:基變換公式、基變換矩陣等
基本知識,相關定理,例題分析,
基本知識
定義1 設向量組
和
是n維向量空間V的兩個基,若它們之間的關係可表示為
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易知,
是可逆矩陣,否則
即
不是n維向量空間V的基,另外,
是從
到基
的過渡矩陣,即
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相關定理
定理設向量空間V的一組基
到另一組基
的過渡矩陣為
,V中一個向量在這兩組基下的坐標分別為
和
,則
,我們也稱
為坐標變換公式,同時也有
.
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例題分析
例1 設向量組
和
是R3的兩個基,且有
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解: 由
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