The theorem state that the eigenvalues of a symmetric are real. [ 3 4 | has real eigenvalues 1 & 5 (verified) but why not symmetric? | 1 3 | Rgds
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Hello, Originally Posted by Chris0724 The theorem state that the eigenvalues of a symmetric are real. [ 3 4 | has real eigenvalues 1 & 5 (verified) but why not symmetric? | 1 3 | Rgds This is logic ! But this is different from . This is the converse of the implication. And is not always true.
Originally Posted by Moo Hello, This is logic ! But this is different from . This is the converse of the implication. And is not always true. So in short, i will always get a Real eigenvalues from a symmetric matrix but Real eigenvalues does not meant that the matrix must be symmetric? Thanks!
Originally Posted by Chris0724 So in short, i will always get a Real eigenvalues from a symmetric matrix but Real eigenvalues does not meant that the matrix must be symmetric? Thanks! Exactly ! The symmetry of a matrix is a sufficient but not necessary condition. If it was, you would have an equivalence, not an implication Necessary and sufficient condition - Wikipedia, the free encyclopedia
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