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线性代数基本定理是秩为 r 的 m×n 矩阵A的奇异值分解:
对于矩阵 (有行及列)产生了四个基本线性子空间:
Secondly:
子空间的维数遵从秩-零化度定理.
进一步, 所有这些空间本质地定义于– 不必考虑基的选择 – 抽象向量空间, 算子, 对偶空间 与: 的核与像是的上核与余象.
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