let A be a 4*4 matrix with the characteristic equation(1-λ^4).determine if A is diagonalizable.

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let A be a 4*4 matrix with the characteristic equation(1-λ^4).determine if A is diagonalizable.

1-x^4=0,解为x=1 -1 i(虚数单位),-i,四个不同的特征值,故可对角化.