This section's topic will perhaps seem out of place at first, but we will make the connection soon with eigenvalues and eigenvectors. This is also our first look at one of the central ideas of Chapter R.
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An n-by-n matrix is diagonalizable if and only if the characteristic polynomial factors completely, and the dimension of each eigenspace equals the multiplicity of the eigenvalue. math.la.t.mat.diagonalizable.charpoly