# Complex Matrix, Diagonal Matrix, Left and Right Eigenvectors and Eigenvalues

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5. Let X^-1 AX = D, where D is a diagonal matrix.

(a) Show that the columns of X are right eigenvectors and the conjugate rows of X^-1 are left eigenvectors of A.

(b) Let ... be the eigenvalues of A. Show that there are right eigenvectors x1,. . . , x and left eigenvectors y1, . . , yn such that

A =...

keywords: matrices

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Complex Matrix, Diagonal Matrix, Left and Right Eigenvectors and Eigenvalues are investigated. The solution is detailed and well presented.

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Problem #5

Proof:

(a) Let , where are columns of . From the condition, we know that , where is a diagonal ...

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