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Is it a little awkward to specify a basis in the proof? Are linear operators and matrices technically two different classes of objects that may be linked by some "matrix representation function" wrt a basis? Thanks!

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- Thread starter 1230wc
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- #1

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Is it a little awkward to specify a basis in the proof? Are linear operators and matrices technically two different classes of objects that may be linked by some "matrix representation function" wrt a basis? Thanks!

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(The bases do not have to be orthonormal. You just have to have some inner product defined on the space to talk about self-adjoint.)

But to go the other way, you don't have to say "view matrix A as a linear transformation". An n by m matrix

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