# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 48: Self-Adjoint Linear Operators

November 27, 2016

Posted by on A linear operator is **self-adjoint **iff it is its own adjoint, i.e. iff

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This is equivalent to the condition that the matrix of with respect to any orthonormal basis is Hermitian (the matrix is its own conjugate transpose).

In addition, if is self-adjoint, then there exists an *orthonormal eigenbasis* for such that the matrix representation of with respect to is a diagonal matrix with real entries.

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