If A is a unitary matrix, then all its eigen values are 1.
True or false with full explanation
If A is a unitary matrix, then all its Eigen values are 1.
this statement is true because:
The eigenvalues and eigenvectors of unitary matrices have some special properties.
If U is unitary, then Thus, if
(1)
then also
(2)
Combining (1) and (2) leads to
Assuming , we thus have
Thus, the eigenvalues of a unitary matrix are unimodular, that is, they have norm 1, and hence can be written as for some
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