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The column space and row space are not the same in the example. But I cannot figure out what was wrong in my argument. The row space of a matrix is the vector space spanned by the row vectors of the matrix and the column space of a matrix is the vector space spanned by the column vectors of the...

I have not said that the eigenspace of eigenvalue ##0## is ##\{0\}##.

Suppose, ##A## is an idempotent matrix, i.e, ##A^2=A##. 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...