Equivalent Conditions
If U is a square, complex matrix, then the following conditions are equivalent:
- U is unitary
- U * is unitary
- U is invertible, with U –1=U *.
- the columns of U form an orthonormal basis of with respect to the usual inner product
- the rows of U form an orthonormal basis of with respect to the usual inner product
- U is an isometry with respect to the usual norm
- U is a normal matrix with eigenvalues lying on the unit circle.
Read more about this topic: Unitary Matrix
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