1. introduction

对于一个 M22 矩阵空间,其 dimM22=4,基的构成如下:

{(1000)(0010)(0100)(0001)}

则:M22≅R4

对于 P3 多项式空间,也即:P3:at3+bt2+ct+d,其基也有如下的四个元素构成:

{t3,t2,t1,1}

同样地,也有 P3≅R4

定理:两个有限维空间是同构的 ⇔ 它们的维度相同。

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