Question

In: Advanced Math

If v is an eigenvector for a matrix A, can v be associated with two different...

If v is an eigenvector for a matrix A, can v be associated with two different eigenvalues? Prove your answer.

Expert Solution

cannot be associate with two eigenvalues of the matrix .

Proof : Suppose the eigenvector associates with two eigenvalues of which are and that is

, as is an eigen vector so it is non-zero .

a contradiction to .

Hence cannot be associate with two eigenvalues of the matrix .

.

If you have any doubt please comment .

Colby Messinger answered 1 year ago

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