Suppose, ##A## is an idempotent matrix, i.e, ##A^2=A##.(adsbygoogle = window.adsbygoogle || []).push({});

For idempotent matrix, the eigenvalues are ##1## and ##0##.

Here, the eigenspace corresponding to eigenvalue ##1## is the column space, and the eigenspace corresponding to eigenvalue ##0## is the null space.

But eigenspaces for distinct eigenvalues of a matrix have intersection ##\{0\}##.

So, null space and column space are complementary for idempotent matrix. That means the row space and column space are the same for idempotent matrix.

Is this argument correct?

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# I Are the columns space and row space same for idempotent matrix?

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