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Math Help - eigenvector u+v

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    eigenvector u+v

    let A be an nxn matrix and suppose that u and v are eigenvectors of A,both with corresponding eigenvalue y.Prove that if u+v is not equal to 0n , then u+v is also an eigenvector of A with corresponding eigenvalue y
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    Quote Originally Posted by math8553 View Post
    let A be an nxn matrix and suppose that u and v are eigenvectors of A,both with corresponding eigenvalue y.Prove that if u+v is not equal to 0n , then u+v is also an eigenvector of A with corresponding eigenvalue y
    By definition A\bold{u} = y\bold{u} and A\bold{v} = y\bold{v}.
    This means, A\bold{u} + A\bold{v} = y\bold{u}+y\bold{v}\implies A(\bold{u}+\bold{v}) = y(\bold{u}+\bold{v})
    Thus, if \bold{u}+\bold{v}\not = 0 then it is an eigenvector with eigenvalue y.
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