If I am given a matrix, and told to determine if it has an orthogonal eigenbasis, is it enough to say yay/nay base on if it is symmetric or not?
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I guess I should ask the question differently... A matrix can have an orthogonal eigenbasis if it is not symmetrical. But are symmetrical matrices guaranteed to have a orthogonal eigenbasis?
Originally Posted by MrJank I guess I should ask the question differently... A matrix can have an orthogonal eigenbasis if it is not symmetrical. But are symmetrical matrices guaranteed to have a orthogonal eigenbasis? real symmetric matrices are guaranteed to have an orthogonal eigenbasis.