Eigenvalues of a matrix are given how to find whether its unitary or not
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know that a unitary matrix can be defined as a square complex matrix AA, such that
AA∗=A∗A=IAA∗=A∗A=I
where
A∗A∗ is the conjugate transpose of AA, and
II is the identity matrix
Furthermore, for a square matrix AA, the eigenvalue equation is expressed by
Av=λvAv=λv
If I use the relationship uv=v∗uuv=v∗u and take the conjugate transpose of this equation then
v∗A∗=λ∗v∗
AA∗=A∗A=IAA∗=A∗A=I
where
A∗A∗ is the conjugate transpose of AA, and
II is the identity matrix
Furthermore, for a square matrix AA, the eigenvalue equation is expressed by
Av=λvAv=λv
If I use the relationship uv=v∗uuv=v∗u and take the conjugate transpose of this equation then
v∗A∗=λ∗v∗
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