一道线性代数中关于线性空间的题:设W是P(n*n)的全体由AB-BA的矩阵所生成的子空间,证明dimW=n^2-1A,B属于P,等号后面是n的平方减1.麻烦的话给个思路.实在没思路,我觉得W是线性空间都很难证
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![一道线性代数中关于线性空间的题:设W是P(n*n)的全体由AB-BA的矩阵所生成的子空间,证明dimW=n^2-1A,B属于P,等号后面是n的平方减1.麻烦的话给个思路.实在没思路,我觉得W是线性空间都很难证](/uploads/image/z/2651026-58-6.jpg?t=%E4%B8%80%E9%81%93%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E4%B8%AD%E5%85%B3%E4%BA%8E%E7%BA%BF%E6%80%A7%E7%A9%BA%E9%97%B4%E7%9A%84%E9%A2%98%EF%BC%9A%E8%AE%BEW%E6%98%AFP%EF%BC%88n%2An%EF%BC%89%E7%9A%84%E5%85%A8%E4%BD%93%E7%94%B1AB-BA%E7%9A%84%E7%9F%A9%E9%98%B5%E6%89%80%E7%94%9F%E6%88%90%E7%9A%84%E5%AD%90%E7%A9%BA%E9%97%B4%2C%E8%AF%81%E6%98%8EdimW%3Dn%5E2-1A%2CB%E5%B1%9E%E4%BA%8EP%2C%E7%AD%89%E5%8F%B7%E5%90%8E%E9%9D%A2%E6%98%AFn%E7%9A%84%E5%B9%B3%E6%96%B9%E5%87%8F1.%E9%BA%BB%E7%83%A6%E7%9A%84%E8%AF%9D%E7%BB%99%E4%B8%AA%E6%80%9D%E8%B7%AF.%E5%AE%9E%E5%9C%A8%E6%B2%A1%E6%80%9D%E8%B7%AF%2C%E6%88%91%E8%A7%89%E5%BE%97W%E6%98%AF%E7%BA%BF%E6%80%A7%E7%A9%BA%E9%97%B4%E9%83%BD%E5%BE%88%E9%9A%BE%E8%AF%81)
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